Finite Group Databasebeta

← Group #13166877

Character table — Group #13166877

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size111144444444488889999121212121212121224242424242424243636363636111144444444488889999121212121212121224242424242424243636363636111144444444488889999121212121212121224242424242424243636363636
order12222336666666666222222444444661212121212122444436666336666666666666666121212121212661212121212126121212123666633666666666666666612121212121266121212121212612121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111-1-111-1-11111-1-1-1-11-1-1-1-111111111111111111111111-1-111-1-11111-1-1-1-11-1-1-1-111111111111111111111111-1-111-1-11111-1-1-1-11-1-1-1-1
χ3111111111111111111111-1-111-1-111-1-1-1-111111-1-1-1-1111111111111111111111-1-111-1-111-1-1-1-111111-1-1-1-1111111111111111111111-1-111-1-111-1-1-1-111111-1-1-1-1
χ4111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ51111-111111111-1-1-1-111111111-1-1-1-111-1-111-1-1-111-1-11111-111111111-1-1-1-111111111-1-1-1-111-1-111-1-1-111-1-11111-111111111-1-1-1-111111111-1-1-1-111-1-111-1-1-111-1-1
χ61111-111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1111111-111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1111111-111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-111
χ71111-111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1111111-111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1111111-111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-111
χ81111-111111111-1-1-1-11111-1-1-1-11111-1-111-1-111-111-1-11111-111111111-1-1-1-11111-1-1-1-11111-1-111-1-111-111-1-11111-111111111-1-1-1-11111-1-1-1-11111-1-111-1-111-111-1-1
χ922222222222222222-2-2-2-20000000000000000-2000022222222222222222-2-2-2-20000000000000000-2000022222222222222222-2-2-2-20000000000000000-20000
χ102222-222222222-2-2-2-2-2-2-2-20000000000000000200002222-222222222-2-2-2-2-2-2-2-20000000000000000200002222-222222222-2-2-2-2-2-2-2-2000000000000000020000
χ1122-2-202222-2-2-2-200002-22-20000002i−2i0000002i−2i0000022-2-202222-2-2-2-200002-22-20000002i−2i0000002i−2i0000022-2-202222-2-2-2-200002-22-20000002i−2i0000002i−2i00000
χ1222-2-202222-2-2-2-200002-22-2000000−2i2i000000−2i2i0000022-2-202222-2-2-2-200002-22-2000000−2i2i000000−2i2i0000022-2-202222-2-2-2-200002-22-2000000−2i2i000000−2i2i00000
χ1322-2-202222-2-2-2-20000-22-22002i−2i000000002i−2i000000022-2-202222-2-2-2-20000-22-22002i−2i000000002i−2i000000022-2-202222-2-2-2-20000-22-22002i−2i000000002i−2i0000000
χ1422-2-202222-2-2-2-20000-22-2200−2i2i00000000−2i2i000000022-2-202222-2-2-2-20000-22-2200−2i2i00000000−2i2i000000022-2-202222-2-2-2-20000-22-2200−2i2i00000000−2i2i0000000
χ152-22-2022-2-222-2-2000022-2-200000000000000000002i−2i2-22-2022-2-222-2-2000022-2-200000000000000000002i−2i2-22-2022-2-222-2-2000022-2-200000000000000000002i−2i
χ162-22-2022-2-222-2-2000022-2-20000000000000000000−2i2i2-22-2022-2-222-2-2000022-2-20000000000000000000−2i2i2-22-2022-2-222-2-2000022-2-20000000000000000000−2i2i
χ172-22-2022-2-222-2-20000-2-222000000000000000002-2002-22-2022-2-222-2-20000-2-222000000000000000002-2002-22-2022-2-222-2-20000-2-222000000000000000002-200
χ182-22-2022-2-222-2-20000-2-22200000000000000000-22002-22-2022-2-222-2-20000-2-22200000000000000000-22002-22-2022-2-222-2-20000-2-22200000000000000000-2200
χ192-2-22022-2-2-2-22200002-2-222-20000002-2000000000002-2-22022-2-2-2-22200002-2-222-20000002-2000000000002-2-22022-2-2-2-22200002-2-222-20000002-200000000000
χ202-2-22022-2-2-2-22200002-2-22-22000000-22000000000002-2-22022-2-2-2-22200002-2-22-22000000-22000000000002-2-22022-2-2-2-22200002-2-22-22000000-2200000000000
χ212-2-22022-2-2-2-2220000-222-200002-200002-20000000002-2-22022-2-2-2-2220000-222-200002-200002-20000000002-2-22022-2-2-2-2220000-222-200002-200002-2000000000
χ222-2-22022-2-2-2-2220000-222-20000-220000-220000000002-2-22022-2-2-2-2220000-222-20000-220000-220000000002-2-22022-2-2-2-2220000-222-20000-220000-22000000000
χ23444441-21-2-211-211-2-20000002200220000-1-1-1-100000444441-21-2-211-211-2-20000002200220000-1-1-1-100000444441-21-2-211-211-2-20000002200220000-1-1-1-100000
χ24444441-21-2-211-211-2-2000000-2-200-2-20000111100000444441-21-2-211-211-2-2000000-2-200-2-20000111100000444441-21-2-211-211-2-2000000-2-200-2-20000111100000
χ2544444-21-211-2-21-2-211000022002200-1-1-1-100000000044444-21-211-2-21-2-211000022002200-1-1-1-100000000044444-21-211-2-21-2-211000022002200-1-1-1-1000000000
χ2644444-21-211-2-21-2-2110000-2-200-2-200111100000000044444-21-211-2-21-2-2110000-2-200-2-200111100000000044444-21-211-2-21-2-2110000-2-200-2-2001111000000000
χ274444-41-21-2-211-2-1-1220000002200-2-20000-1-111000004444-41-21-2-211-2-1-1220000002200-2-20000-1-111000004444-41-21-2-211-2-1-1220000002200-2-20000-1-11100000
χ284444-41-21-2-211-2-1-122000000-2-20022000011-1-1000004444-41-21-2-211-2-1-122000000-2-20022000011-1-1000004444-41-21-2-211-2-1-122000000-2-20022000011-1-100000
χ294444-4-21-211-2-2122-1-100002200-2-200-1-1110000000004444-4-21-211-2-2122-1-100002200-2-200-1-1110000000004444-4-21-211-2-2122-1-100002200-2-200-1-111000000000
χ304444-4-21-211-2-2122-1-10000-2-200220011-1-10000000004444-4-21-211-2-2122-1-10000-2-200220011-1-10000000004444-4-21-211-2-2122-1-10000-2-200220011-1-1000000000
χ3144-4-401-21-22-1-123-3000000002i−2i002i−2i0000−ii−ii0000044-4-401-21-22-1-123-3000000002i−2i002i−2i0000−ii−ii0000044-4-401-21-22-1-123-3000000002i−2i002i−2i0000−ii−ii00000
χ3244-4-401-21-22-1-123-300000000−2i2i00−2i2i0000i−ii−i0000044-4-401-21-22-1-123-300000000−2i2i00−2i2i0000i−ii−i0000044-4-401-21-22-1-123-300000000−2i2i00−2i2i0000i−ii−i00000
χ3344-4-401-21-22-1-12-33000000002i−2i00−2i2i0000−iii−i0000044-4-401-21-22-1-12-33000000002i−2i00−2i2i0000−iii−i0000044-4-401-21-22-1-12-33000000002i−2i00−2i2i0000−iii−i00000
χ3444-4-401-21-22-1-12-3300000000−2i2i002i−2i0000i−i−ii0000044-4-401-21-22-1-12-3300000000−2i2i002i−2i0000i−i−ii0000044-4-401-21-22-1-12-3300000000−2i2i002i−2i0000i−i−ii00000
χ354-4-440-212-1-12-21003-300002-2002-200-11-110000000004-4-440-212-1-12-21003-300002-2002-200-11-110000000004-4-440-212-1-12-21003-300002-2002-200-11-11000000000
χ364-4-440-212-1-12-21003-30000-2200-22001-11-10000000004-4-440-212-1-12-21003-30000-2200-22001-11-10000000004-4-440-212-1-12-21003-30000-2200-22001-11-1000000000
χ374-4-440-212-1-12-2100-3300002-200-2200-111-10000000004-4-440-212-1-12-2100-3300002-200-2200-111-10000000004-4-440-212-1-12-2100-3300002-200-2200-111-1000000000
χ384-4-440-212-1-12-2100-330000-22002-2001-1-110000000004-4-440-212-1-12-2100-330000-22002-2001-1-110000000004-4-440-212-1-12-2100-330000-22002-2001-1-11000000000
χ3988-8-80-42-42-244-20000000000000000000000000000088-8-80-42-42-244-20000000000000000000000000000088-8-80-42-42-244-200000000000000000000000000000
χ408-88-802-4-24-42-24000000000000000000000000000008-88-802-4-24-42-24000000000000000000000000000008-88-802-4-24-42-2400000000000000000000000000000
χ418-88-80-424-22-44-2000000000000000000000000000008-88-80-424-22-44-2000000000000000000000000000008-88-80-424-22-44-200000000000000000000000000000
χ428-8-8802-4-244-22-4000000000000000000000000000008-8-8802-4-244-22-4000000000000000000000000000008-8-8802-4-244-22-400000000000000000000000000000
χ43111111111111111111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ4411111111111111111111111-1-111-1-11111-1-1-1-11-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i321+i321+i321+i32
χ45111111111111111111111-1-111-1-111-1-1-1-111111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ46111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ471111-111111111-1-1-1-111111111-1-1-1-111-1-111-1-1-111-1-1−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32
χ481111-111111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-111−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32
χ491111-111111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-111−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32
χ501111-111111111-1-1-1-11111-1-1-1-11111-1-111-1-111-111-1-1−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32
χ5122222222222222222-2-2-2-20000000000000000-20000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i300000000000000001−i30000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i300000000000000001+i30000
χ522222-222222222-2-2-2-2-2-2-2-2000000000000000020000−1+i3−1+i3−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i31−i31−i31−i31−i30000000000000000−1+i30000−1−i3−1−i3−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i31+i31+i31+i31+i30000000000000000−1−i30000
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χ11744-4-401-21-22-1-12-33000000002i−2i00−2i2i0000−iii−i00000−2−2i3−2−2i32+2i32+2i30−1−i321+i3−1−i321+i3−1−i31+i321+i32−1−i33+3i32−3−3i32000000002ζ11−2ζ1100−2ζ112ζ110000−ζ11ζ11ζ11−ζ1100000−2+2i3−2+2i32−2i32−2i30−1+i321−i3−1+i321−i3−1+i31−i321−i32−1+i33−3i32−3+3i32000000002ζ7−2ζ700−2ζ72ζ70000−ζ7ζ7ζ7−ζ700000
χ11844-4-401-21-22-1-12-3300000000−2i2i002i−2i0000i−i−ii00000−2−2i3−2−2i32+2i32+2i30−1−i321+i3−1−i321+i3−1−i31+i321+i32−1−i33+3i32−3−3i3200000000−2ζ112ζ11002ζ11−2ζ110000ζ11−ζ11−ζ11ζ1100000−2+2i3−2+2i32−2i32−2i30−1+i321−i3−1+i321−i3−1+i31−i321−i32−1+i33−3i32−3+3i3200000000−2ζ72ζ7002ζ7−2ζ70000ζ7−ζ7−ζ7ζ700000
χ1194-4-440-212-1-12-21003-300002-2002-200-11-11000000000−2−2i32+2i32+2i3−2−2i301+i3−1−i32−1−i31+i321+i32−1−i31+i3−1−i3200−3−3i323+3i320000−1−i31+i300−1−i31+i3001+i32−1−i321+i32−1−i32000000000−2+2i32−2i32−2i3−2+2i301−i3−1+i32−1+i31−i321−i32−1+i31−i3−1+i3200−3+3i323−3i320000−1+i31−i300−1+i31−i3001−i32−1+i321−i32−1+i32000000000
χ1204-4-440-212-1-12-21003-30000-2200-22001-11-1000000000−2−2i32+2i32+2i3−2−2i301+i3−1−i32−1−i31+i321+i32−1−i31+i3−1−i3200−3−3i323+3i3200001+i3−1−i3001+i3−1−i300−1−i321+i32−1−i321+i32000000000−2+2i32−2i32−2i3−2+2i301−i3−1+i32−1+i31−i321−i32−1+i31−i3−1+i3200−3+3i323−3i3200001−i3−1+i3001−i3−1+i300−1+i321−i32−1+i321−i32000000000
χ1214-4-440-212-1-12-2100-3300002-200-2200-111-1000000000−2−2i32+2i32+2i3−2−2i301+i3−1−i32−1−i31+i321+i32−1−i31+i3−1−i32003+3i32−3−3i320000−1−i31+i3001+i3−1−i3001+i32−1−i32−1−i321+i32000000000−2+2i32−2i32−2i3−2+2i301−i3−1+i32−1+i31−i321−i32−1+i31−i3−1+i32003−3i32−3+3i320000−1+i31−i3001−i3−1+i3001−i32−1+i32−1+i321−i32000000000
χ1224-4-440-212-1-12-2100-330000-22002-2001-1-11000000000−2−2i32+2i32+2i3−2−2i301+i3−1−i32−1−i31+i321+i32−1−i31+i3−1−i32003+3i32−3−3i3200001+i3−1−i300−1−i31+i300−1−i321+i321+i32−1−i32000000000−2+2i32−2i32−2i3−2+2i301−i3−1+i32−1+i31−i321−i32−1+i31−i3−1+i32003−3i32−3+3i3200001−i3−1+i300−1+i31−i300−1+i321−i321−i32−1+i32000000000
χ12388-8-80-42-42-244-200000000000000000000000000000−4−4i3−4−4i34+4i34+4i302+2i3−1−i32+2i3−1−i31+i3−2−2i3−2−2i31+i300000000000000000000000000000−4+4i3−4+4i34−4i34−4i302−2i3−1+i32−2i3−1+i31−i3−2+2i3−2+2i31−i300000000000000000000000000000
χ1248-88-802-4-24-42-2400000000000000000000000000000−4−4i34+4i3−4−4i34+4i30−1−i32+2i31+i3−2−2i32+2i3−1−i31+i3−2−2i300000000000000000000000000000−4+4i34−4i3−4+4i34−4i30−1+i32−2i31−i3−2+2i32−2i3−1+i31−i3−2+2i300000000000000000000000000000
χ1258-88-80-424-22-44-200000000000000000000000000000−4−4i34+4i3−4−4i34+4i302+2i3−1−i3−2−2i31+i3−1−i32+2i3−2−2i31+i300000000000000000000000000000−4+4i34−4i3−4+4i34−4i302−2i3−1+i3−2+2i31−i3−1+i32−2i3−2+2i31−i300000000000000000000000000000
χ1268-8-8802-4-244-22-400000000000000000000000000000−4−4i34+4i34+4i3−4−4i30−1−i32+2i31+i3−2−2i3−2−2i31+i3−1−i32+2i300000000000000000000000000000−4+4i34−4i34−4i3−4+4i30−1+i32−2i31−i3−2+2i3−2+2i31−i3−1+i32−2i300000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.