Finite Group Databasebeta

← Group #13166887

Character table — Group #13166887

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size111122444444448888181818181818181818181818242424242424242424242424111122444444448888181818181818181818181818242424242424242424242424111122444444448888181818181818181818181818242424242424242424242424
order1222223366666666664444888888882244666612121212366666336666666666121212122424242424242424661212666612121212366666336666666666121212122424242424242424661212666612121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-11111111111111111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-11111111111111111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111
χ51111-1-111111111-1-1-1-11-1-111111-1-1-1-111-1-11111-1-1-1-11111-1-111111111-1-1-1-11-1-111111-1-1-1-111-1-11111-1-1-1-11111-1-111111111-1-1-1-11-1-111111-1-1-1-111-1-11111-1-1-1-1
χ61111-1-111111111-1-1-1-11-1-111111-1-1-1-1-1-111-1-1-1-111111111-1-111111111-1-1-1-11-1-111111-1-1-1-1-1-111-1-1-1-111111111-1-111111111-1-1-1-11-1-111111-1-1-1-1-1-111-1-1-1-11111
χ71111-1-111111111-1-1-1-11-1-11-1-1-1-111111-1-1111-1-1-1-1111111-1-111111111-1-1-1-11-1-11-1-1-1-111111-1-1111-1-1-1-1111111-1-111111111-1-1-1-11-1-11-1-1-1-111111-1-1111-1-1-1-111
χ81111-1-111111111-1-1-1-11-1-11-1-1-1-11111-111-1-1-11111-1-11111-1-111111111-1-1-1-11-1-11-1-1-1-11111-111-1-1-11111-1-11111-1-111111111-1-1-1-11-1-11-1-1-1-11111-111-1-1-11111-1-1
χ9222222222222222222-2-2-2-200000000000000000000222222222222222222-2-2-2-200000000000000000000222222222222222222-2-2-2-200000000000000000000
χ102222-2-222222222-2-2-2-2-222-2000000000000000000002222-2-222222222-2-2-2-2-222-2000000000000000000002222-2-222222222-2-2-2-2-222-200000000000000000000
χ1122-2-2002222-2-2-2-2000002i−2i022−2−2−i2−i2i2i200000000000022-2-2002222-2-2-2-2000002i−2i022−2−2−i2−i2i2i200000000000022-2-2002222-2-2-2-2000002i−2i022−2−2−i2−i2i2i2000000000000
χ1222-2-2002222-2-2-2-2000002i−2i0−2−222i2i2−i2−i200000000000022-2-2002222-2-2-2-2000002i−2i0−2−222i2i2−i2−i200000000000022-2-2002222-2-2-2-2000002i−2i0−2−222i2i2−i2−i2000000000000
χ1322-2-2002222-2-2-2-200000−2i2i022−2−2i2i2−i2−i200000000000022-2-2002222-2-2-2-200000−2i2i022−2−2i2i2−i2−i200000000000022-2-2002222-2-2-2-200000−2i2i022−2−2i2i2−i2−i2000000000000
χ1422-2-2002222-2-2-2-200000−2i2i0−2−222−i2−i2i2i200000000000022-2-2002222-2-2-2-200000−2i2i0−2−222−i2−i2i2i200000000000022-2-2002222-2-2-2-200000−2i2i0−2−222−i2−i2i2i2000000000000
χ152-22-22-222-2-2-2-22222-2-200002−22−22−22−20000000000002-22-22-222-2-2-2-22222-2-200002−22−22−22−20000000000002-22-22-222-2-2-2-22222-2-200002−22−22−22−2000000000000
χ162-22-22-222-2-2-2-22222-2-20000−22−22−22−220000000000002-22-22-222-2-2-2-22222-2-20000−22−22−22−220000000000002-22-22-222-2-2-2-22222-2-20000−22−22−22−22000000000000
χ172-22-2-2222-2-2-2-222-2-22200002−22−2−22−220000000000002-22-2-2222-2-2-2-222-2-22200002−22−2−22−220000000000002-22-2-2222-2-2-2-222-2-22200002−22−2−22−22000000000000
χ182-22-2-2222-2-2-2-222-2-2220000−22−222−22−20000000000002-22-2-2222-2-2-2-222-2-2220000−22−222−22−20000000000002-22-2-2222-2-2-2-222-2-2220000−22−222−22−2000000000000
χ192-2-220022-2-222-2-20000200-200002i−2i−2i2i0000000000002-2-220022-2-222-2-20000200-200002i−2i−2i2i0000000000002-2-220022-2-222-2-20000200-200002i−2i−2i2i000000000000
χ202-2-220022-2-222-2-20000200-20000−2i2i2i−2i0000000000002-2-220022-2-222-2-20000200-20000−2i2i2i−2i0000000000002-2-220022-2-222-2-20000200-20000−2i2i2i−2i000000000000
χ212-2-220022-2-222-2-20000-20022-2-2200000000000000002-2-220022-2-222-2-20000-20022-2-2200000000000000002-2-220022-2-222-2-20000-20022-2-220000000000000000
χ222-2-220022-2-222-2-20000-2002-222-200000000000000002-2-220022-2-222-2-20000-2002-222-200000000000000002-2-220022-2-222-2-20000-2002-222-20000000000000000
χ234444441-21-21-21-21-21-2000000000000020200-1-100-1-14444441-21-21-21-21-21-2000000000000020200-1-100-1-14444441-21-21-21-21-21-2000000000000020200-1-100-1-1
χ244444441-21-21-21-21-21-20000000000000-20-2001100114444441-21-21-21-21-21-20000000000000-20-2001100114444441-21-21-21-21-21-20000000000000-20-200110011
χ25444444-21-21-21-21-21-210000000000002020-1-100-1-100444444-21-21-21-21-21-210000000000002020-1-100-1-100444444-21-21-21-21-21-210000000000002020-1-100-1-100
χ26444444-21-21-21-21-21-21000000000000-20-2011001100444444-21-21-21-21-21-21000000000000-20-2011001100444444-21-21-21-21-21-21000000000000-20-2011001100
χ274444-4-41-21-21-21-2-12-12000000000000020-200-1-100114444-4-41-21-21-21-2-12-12000000000000020-200-1-100114444-4-41-21-21-21-2-12-12000000000000020-200-1-10011
χ284444-4-41-21-21-21-2-12-120000000000000-202001100-1-14444-4-41-21-21-21-2-12-120000000000000-202001100-1-14444-4-41-21-21-21-2-12-120000000000000-202001100-1-1
χ294444-4-4-21-21-21-212-12-100000000000020-20-1-10011004444-4-4-21-21-21-212-12-100000000000020-20-1-10011004444-4-4-21-21-21-212-12-100000000000020-20-1-1001100
χ304444-4-4-21-21-21-212-12-1000000000000-20201100-1-1004444-4-4-21-21-21-212-12-1000000000000-20201100-1-1004444-4-4-21-21-21-212-12-1000000000000-20201100-1-100
χ314-44-44-41-2-12-121-21-2-12000000000000000000−i3i300−i3i34-44-44-41-2-12-121-21-2-12000000000000000000−i3i300−i3i34-44-44-41-2-12-121-21-2-12000000000000000000−i3i300−i3i3
χ324-44-44-41-2-12-121-21-2-12000000000000000000i3−i300i3−i34-44-44-41-2-12-121-21-2-12000000000000000000i3−i300i3−i34-44-44-41-2-12-121-21-2-12000000000000000000i3−i300i3−i3
χ334-44-44-4-212-12-1-21-212-10000000000000000−i3i300−i3i3004-44-44-4-212-12-1-21-212-10000000000000000−i3i300−i3i3004-44-44-4-212-12-1-21-212-10000000000000000−i3i300−i3i300
χ344-44-44-4-212-12-1-21-212-10000000000000000i3−i300i3−i3004-44-44-4-212-12-1-21-212-10000000000000000i3−i300i3−i3004-44-44-4-212-12-1-21-212-10000000000000000i3−i300i3−i300
χ354-44-4-441-2-12-121-2-121-2000000000000000000−i3i300i3−i34-44-4-441-2-12-121-2-121-2000000000000000000−i3i300i3−i34-44-4-441-2-12-121-2-121-2000000000000000000−i3i300i3−i3
χ364-44-4-441-2-12-121-2-121-2000000000000000000i3−i300−i3i34-44-4-441-2-12-121-2-121-2000000000000000000i3−i300−i3i34-44-4-441-2-12-121-2-121-2000000000000000000i3−i300−i3i3
χ374-44-4-44-212-12-1-212-1-210000000000000000−i3i300i3−i3004-44-4-44-212-12-1-212-1-210000000000000000−i3i300i3−i3004-44-4-44-212-12-1-212-1-210000000000000000−i3i300i3−i300
χ384-44-4-44-212-12-1-212-1-210000000000000000i3−i300−i3i3004-44-4-44-212-12-1-212-1-210000000000000000i3−i300−i3i3004-44-4-44-212-12-1-212-1-210000000000000000i3−i300−i3i300
χ3988-8-8002-42-4-24-24000000000000000000000000000088-8-8002-42-4-24-24000000000000000000000000000088-8-8002-42-4-24-240000000000000000000000000000
χ4088-8-800-42-424-24-2000000000000000000000000000088-8-800-42-424-24-2000000000000000000000000000088-8-800-42-424-24-20000000000000000000000000000
χ418-8-88002-4-242-4-2400000000000000000000000000008-8-88002-4-242-4-2400000000000000000000000000008-8-88002-4-242-4-240000000000000000000000000000
χ428-8-8800-424-2-424-200000000000000000000000000008-8-8800-424-2-424-200000000000000000000000000008-8-8800-424-2-424-20000000000000000000000000000
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
χ44111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−1+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+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−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−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32
χ451111111111111111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-1−1+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+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+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−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ461111111111111111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111−1+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−i32−1+i321−i32−1+i321−i321−i32−1+i32−1+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−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32
χ471111-1-111111111-1-1-1-11-1-111111-1-1-1-111-1-11111-1-1-1-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−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+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ481111-1-111111111-1-1-1-11-1-111111-1-1-1-1-1-111-1-1-1-11111−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−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+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ491111-1-111111111-1-1-1-11-1-11-1-1-1-111111-1-1111-1-1-1-111−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32
χ501111-1-111111111-1-1-1-11-1-11-1-1-1-11111-111-1-1-11111-1-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ51222222222222222222-2-2-2-200000000000000000000−1+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+i3−1+i31−i31−i31−i31−i300000000000000000000−1−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−i3−1−i31+i31+i31+i31+i300000000000000000000
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χ12388-8-8002-42-4-24-240000000000000000000000000000−4−4i3−4−4i34+4i34+4i300−1−i32+2i3−1−i32+2i31+i3−2−2i31+i3−2−2i30000000000000000000000000000−4+4i3−4+4i34−4i34−4i300−1+i32−2i3−1+i32−2i31−i3−2+2i31−i3−2+2i30000000000000000000000000000
χ12488-8-800-42-424-24-20000000000000000000000000000−4−4i3−4−4i34+4i34+4i3002+2i3−1−i32+2i3−1−i3−2−2i31+i3−2−2i31+i30000000000000000000000000000−4+4i3−4+4i34−4i34−4i3002−2i3−1+i32−2i3−1+i3−2+2i31−i3−2+2i31−i30000000000000000000000000000
χ1258-8-88002-4-242-4-240000000000000000000000000000−4−4i34+4i34+4i3−4−4i300−1−i32+2i31+i3−2−2i3−1−i32+2i31+i3−2−2i30000000000000000000000000000−4+4i34−4i34−4i3−4+4i300−1+i32−2i31−i3−2+2i3−1+i32−2i31−i3−2+2i30000000000000000000000000000
χ1268-8-8800-424-2-424-20000000000000000000000000000−4−4i34+4i34+4i3−4−4i3002+2i3−1−i3−2−2i31+i32+2i3−1−i3−2−2i31+i30000000000000000000000000000−4+4i34−4i34−4i3−4+4i3002−2i3−1+i3−2+2i31−i32−2i3−1+i3−2+2i31−i30000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.