Finite Group Databasebeta

← Group #13147920

Character table — Group #13147920

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order1222344446661212121241212121233666666121212123666121212121212121212121212121212121212121212122222444422444444666666121212121212121212126121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11-1-11-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-111-1-1111-1-1-1-1-11-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-11-111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-11111111-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-111-1-1-1-111111-1-111-1-1-1-111-1-111-1-1
χ61111111-1-11111111-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1111-11-111-1-11111-1-1-1-1-1-111-1-111
χ71111111-1-11111111-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1111-1-1-1-111-1-1-1-1111111-1-1-1-111
χ81111111-1-11111111-1-1-1-1-111111111-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1111-1-1-1-111-1-11111-1-11111-1-1
χ911111-1-111111-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-11-11-1-11-11111-1-1-1-111-1-1-1-1111-11-1
χ1011111-1-111111-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-111111-1-1-11-1-1111-1-111-1-111-1-111-1-1-11-11
χ1111111-1-111111-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11-11111-1-111-1-111-1-111-1-111-11-11
χ1211111-1-111111-1-1-1-1-111-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-11-1-1-1-1-1-11111-1-11111-1-11-11-1
χ1311111-1-1-1-1111-1-1-1-11-1-11111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1111111-1-1-1-111-1-1-1-11-1-11
χ1411111-1-1-1-1111-1-1-1-11-1-11111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-11-111111-1-1-1-1-1-1-1-1111111-111-1
χ1511111-1-1-1-1111-1-1-1-11-1-11111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-11-111-1-1-11-1-111111111-1-1-1-1-1-1-111-1
χ1611111-1-1-1-1111-1-1-1-11-1-11111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-11-11-1-1-1-1-1-1-11111-1-111111-1-11
χ172222222222222222222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1002200222000002000-1-1-1-1000000-1-1-1-10000
χ182222222222222222222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-100-2-200-2-2-200000-2000111100000011110000
χ19222222222222222222222-1222-1-1-122222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000020220020000000000000000-1-1-1-1
χ20222222222222222222222-1222-1-1-122222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000-20-2-200-200000000000000001111
χ212222222-2-22222222-2-2-2-2-22-1-1-1222-11111-1-1-1-1-1-11122-2-2-2-2-1-1-1-11111111100220022-200000-2000-1-111000000-1-1110000
χ222222222-2-22222222-2-2-2-2-22-1-1-1222-11111-1-1-1-1-1-11122-2-2-2-2-1-1-1-11111111100-2-200-2-2200000200011-1-100000011-1-10000
χ232222222-2-22222222-2-2-2-2-2-1222-1-1-12-2-2-2-2-1-1-1-122-2-2-1-11111-1-1-1-11111111100000000020-2-20020000000000000000-1-111
χ242222222-2-22222222-2-2-2-2-2-1222-1-1-12-2-2-2-2-1-1-1-122-2-2-1-11111-1-1-1-111111111000000000-202200-2000000000000000011-1-1
χ2522222-2-222222-2-2-2-2-222-2-22-1-1-1222-1-1-1-1-1-1-1-1-11111-2-222-2-21111-1-1-1-11111002200-2-2-2000002000-1-11100000011-1-10000
χ2622222-2-222222-2-2-2-2-222-2-22-1-1-1222-1-1-1-1-1-1-1-1-11111-2-222-2-21111-1-1-1-1111100-2-20022200000-200011-1-1000000-1-1110000
χ2722222-2-222222-2-2-2-2-222-2-2-1222-1-1-122222-1-1-1-1-2-2-2-211-1-1111111-1-1-1-11111000000000202-200-20000000000000000-11-11
χ2822222-2-222222-2-2-2-2-222-2-2-1222-1-1-122222-1-1-1-1-2-2-2-211-1-1111111-1-1-1-11111000000000-20-2200200000000000000001-11-1
χ2922222-2-2-2-2222-2-2-2-22-2-2222-1-1-1222-11111-1-1-1-111-1-1-2-2-2-22211111111-1-1-1-1002200-2-2200000-2000-1-1-1-100000011110000
χ3022222-2-2-2-2222-2-2-2-22-2-2222-1-1-1222-11111-1-1-1-111-1-1-2-2-2-22211111111-1-1-1-100-2-20022-20000020001111000000-1-1-1-10000
χ3122222-2-2-2-2222-2-2-2-22-2-222-1222-1-1-12-2-2-2-2-1-1-1-1-2-2221111-1-111111111-1-1-1-100000000020-2200-20000000000000000-111-1
χ3222222-2-2-2-2222-2-2-2-22-2-222-1222-1-1-12-2-2-2-2-1-1-1-1-2-2221111-1-111111111-1-1-1-1000000000-202-200200000000000000001-1-11
χ3322-2-22002i−2i2-2-2000002i−2i00222-22-2-2-22i2i−2i−2i22-2-20000002i−2i0000002i2i−2i−2i00002-2002i−2i00000000002-20000002i−2i0000000000
χ3422-2-22002i−2i2-2-2000002i−2i00222-22-2-2-22i2i−2i−2i22-2-20000002i−2i0000002i2i−2i−2i0000-2200−2i2i0000000000-22000000−2i2i0000000000
χ3522-2-2200−2i2i2-2-200000−2i2i00222-22-2-2-2−2i−2i2i2i22-2-2000000−2i2i000000−2i−2i2i2i00002-200−2i2i00000000002-2000000−2i2i0000000000
χ3622-2-2200−2i2i2-2-200000−2i2i00222-22-2-2-2−2i−2i2i2i22-2-2000000−2i2i000000−2i−2i2i2i0000-22002i−2i0000000000-220000002i−2i0000000000
χ372-22-222i−2i00-22-22i2i−2i−2i0000022-22-22-2-200002-22-22i−2i002i−2i00002i2i−2i−2i00000000002-2002i−2i00000000002-2000000002i−2i000000
χ382-22-222i−2i00-22-22i2i−2i−2i0000022-22-22-2-200002-22-22i−2i002i−2i00002i2i−2i−2i0000000000-2200−2i2i0000000000-2200000000−2i2i000000
χ392-22-222i−2i00-22-22i2i−2i−2i000002-11-1-22-213−33−3-11-11−ii−i3i32i−2i0000−i−iii3−33−3−i3−i3i3i3002-2002i−2i0000000000-11−i3i3000000−ii3−30000
χ402-22-222i−2i00-22-22i2i−2i−2i000002-11-1-22-213−33−3-11-11−ii−i3i32i−2i0000−i−iii3−33−3−i3−i3i3i300-2200−2i2i00000000001-1i3−i3000000i−i−330000
χ412-22-222i−2i00-22-22i2i−2i−2i000002-11-1-22-21−33−33-11-11−iii3−i32i−2i0000−i−iii−33−33i3i3−i3−i3002-2002i−2i0000000000-11i3−i3000000−ii−330000
χ422-22-222i−2i00-22-22i2i−2i−2i000002-11-1-22-21−33−33-11-11−iii3−i32i−2i0000−i−iii−33−33i3i3−i3−i300-2200−2i2i00000000001-1−i3i3000000i−i3−30000
χ432-22-22−2i2i00-22-2−2i−2i2i2i0000022-22-22-2-200002-22-2−2i2i00−2i2i0000−2i−2i2i2i00000000002-200−2i2i00000000002-200000000−2i2i000000
χ442-22-22−2i2i00-22-2−2i−2i2i2i0000022-22-22-2-200002-22-2−2i2i00−2i2i0000−2i−2i2i2i0000000000-22002i−2i0000000000-22000000002i−2i000000
χ452-22-22−2i2i00-22-2−2i−2i2i2i000002-11-1-22-213−33−3-11-11i−ii3−i3−2i2i0000ii−i−i3−33−3i3i3−i3−i3002-200−2i2i0000000000-11i3−i3000000i−i3−30000
χ462-22-22−2i2i00-22-2−2i−2i2i2i000002-11-1-22-213−33−3-11-11i−ii3−i3−2i2i0000ii−i−i3−33−3i3i3−i3−i300-22002i−2i00000000001-1−i3i3000000−ii−330000
χ472-22-22−2i2i00-22-2−2i−2i2i2i000002-11-1-22-21−33−33-11-11i−i−i3i3−2i2i0000ii−i−i−33−33−i3−i3i3i3002-200−2i2i0000000000-11−i3i3000000i−i−330000
χ482-22-22−2i2i00-22-2−2i−2i2i2i000002-11-1-22-21−33−33-11-11i−i−i3i3−2i2i0000ii−i−i−33−33−i3−i3i3i300-22002i−2i00000000001-1i3−i3000000−ii3−30000
χ49444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2-2-2111111111111000000000000000000000000000000000000
χ504444444-4-44444444-4-4-4-4-4-2-2-2-2-2-2-2-222221111-2-222-2-222221111-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ5144444-4-444444-4-4-4-4-444-4-4-2-2-2-2-2-2-2-2-2-2-2-21111222222-2-222-1-1-1-11111-1-1-1-1000000000000000000000000000000000000
χ5244444-4-4-4-4444-4-4-4-44-4-444-2-2-2-2-2-2-2-22222111122-2-22222-2-2-1-1-1-1-1-1-1-11111000000000000000000000000000000000000
χ5344-4-44004i−4i4-4-4000004i−4i004-2-224-4-42−2i−2i2i2i-2-2220000004i−4i000000−2i−2i2i2i0000000000000000000000000000000000000000
χ5444-4-44004i−4i4-4-4000004i−4i00-244-4-222-44i4i−4i−4i-2-222000000−2i2i000000−2i−2i2i2i0000000000000000000000000000000000000000
χ5544-4-44004i−4i4-4-4000004i−4i00-2-2-22-2222−2i−2i2i2i11-1-1000000−2i2i003-33-3ii−i−i3i−3i3i−3i000000000000000000000000000000000000
χ5644-4-44004i−4i4-4-4000004i−4i00-2-2-22-2222−2i−2i2i2i11-1-1000000−2i2i00-33-33ii−i−i−3i3i−3i3i000000000000000000000000000000000000
χ5744-4-4400−4i4i4-4-400000−4i4i004-2-224-4-422i2i−2i−2i-2-222000000−4i4i0000002i2i−2i−2i0000000000000000000000000000000000000000
χ5844-4-4400−4i4i4-4-400000−4i4i00-244-4-222-4−4i−4i4i4i-2-2220000002i−2i0000002i2i−2i−2i0000000000000000000000000000000000000000
χ5944-4-4400−4i4i4-4-400000−4i4i00-2-2-22-22222i2i−2i−2i11-1-10000002i−2i003-33-3−i−iii−3i3i−3i3i000000000000000000000000000000000000
χ6044-4-4400−4i4i4-4-400000−4i4i00-2-2-22-22222i2i−2i−2i11-1-10000002i−2i00-33-33−i−iii3i−3i3i−3i000000000000000000000000000000000000
χ614-44-444i−4i00-44-44i4i−4i−4i00000-24-442-22-40000-22-224i−4i00−2i2i0000−2i−2i2i2i00000000000000000000000000000000000000000000
χ624-44-444i−4i00-44-44i4i−4i−4i00000-2-22-22-22223−2323−231-11-1−2i2i−2i32i3−2i2i0000ii−i−i−33−33i3i3−i3−i3000000000000000000000000000000000000
χ634-44-444i−4i00-44-44i4i−4i−4i00000-2-22-22-222−2323−23231-11-1−2i2i2i3−2i3−2i2i0000ii−i−i3−33−3−i3−i3i3i3000000000000000000000000000000000000
χ644-44-44−4i4i00-44-4−4i−4i4i4i00000-24-442-22-40000-22-22−4i4i002i−2i00002i2i−2i−2i00000000000000000000000000000000000000000000
χ654-44-44−4i4i00-44-4−4i−4i4i4i00000-2-22-22-22223−2323−231-11-12i−2i2i3−2i32i−2i0000−i−iii−33−33−i3−i3i3i3000000000000000000000000000000000000
χ664-44-44−4i4i00-44-4−4i−4i4i4i00000-2-22-22-222−2323−23231-11-12i−2i−2i32i32i−2i0000−i−iii3−33−3i3i3−i3−i3000000000000000000000000000000000000
χ674-4-4440000-4-4400000000044-4-4-4-44400004-4-440000000000000000000000000000000000000000000000000000000000
χ684-4-4440000-4-440000000004-222-4-44-2−2i32i32i3−2i3-222-200000000000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ694-4-4440000-4-440000000004-222-4-44-22i3−2i3−2i32i3-222-2000000000000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ704-4-4440000-4-44000000000-24-4-422-240000-222-20000000023−230000000023−23−2323000000000000000000000000000000000000
χ714-4-4440000-4-44000000000-24-4-422-240000-222-200000000−232300000000−232323−23000000000000000000000000000000000000
χ724-4-4440000-4-44000000000-2-22222-2-2−2i32i32i3−2i31-1-110000000023−233i−3i−3i3ii3−i3−i3i3−333−3000000000000000000000000000000000000
χ734-4-4440000-4-44000000000-2-22222-2-2−2i32i32i3−2i31-1-1100000000−2323−3i3i3i−3ii3−i3−i3i33−3−33000000000000000000000000000000000000
χ744-4-4440000-4-44000000000-2-22222-2-22i3−2i3−2i32i31-1-110000000023−23−3i3i3i−3i−i3i3i3−i3−333−3000000000000000000000000000000000000
χ754-4-4440000-4-44000000000-2-22222-2-22i3−2i3−2i32i31-1-1100000000−23233i−3i−3i3i−i3i3i3−i33−3−33000000000000000000000000000000000000
χ766666-36666-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000002200220000200200-1-10000-1-1-1-1-1-100000000
χ776666-36666-3-3-3-3-3-3-36-3-3-3-300000000000000000000000000000000000000-2-200-2-20000-200-20011000011111100000000
χ786666-366-6-6-3-3-3-3-3-3-3-63333000000000000000000000000000000000000002200-2-20000200-200-1-10000-1-1111100000000
χ796666-366-6-6-3-3-3-3-3-3-3-6333300000000000000000000000000000000000000-2-200220000-20020011000011-1-1-1-100000000
χ806666-3-6-666-3-3-33333-6-3-333000000000000000000000000000000000000002200220000-200-200-1-1000011-1-11100000000
χ816666-3-6-666-3-3-33333-6-3-33300000000000000000000000000000000000000-2-200-2-20000200200110000-1-111-1-100000000
χ826666-3-6-6-6-6-3-3-33333633-3-3000000000000000000000000000000000000002200-2-20000-200200-1-100001111-1-100000000
χ836666-3-6-6-6-6-3-3-33333633-3-300000000000000000000000000000000000000-2-200220000200-200110000-1-1-1-11100000000
χ8466-6-6-3006i−6i-333−3i33i3−3i33i30−3i3i33−33000000000000000000000000000000000000002-2002i−2i0000000000-110000−i3i3−ii3−300000000
χ8566-6-6-3006i−6i-333−3i33i3−3i33i30−3i3i33−3300000000000000000000000000000000000000-2200−2i2i00000000001-10000i3−i3i−i−3300000000
χ8666-6-6-3006i−6i-3333i3−3i33i3−3i30−3i3i−3333000000000000000000000000000000000000002-2002i−2i0000000000-110000i3−i3−ii−3300000000
χ8766-6-6-3006i−6i-3333i3−3i33i3−3i30−3i3i−333300000000000000000000000000000000000000-2200−2i2i00000000001-10000−i3i3i−i3−300000000
χ8866-6-6-300−6i6i-333−3i33i3−3i33i303i−3i−3333000000000000000000000000000000000000002-200−2i2i0000000000-110000−i3i3i−i−3300000000
χ8966-6-6-300−6i6i-333−3i33i3−3i33i303i−3i−333300000000000000000000000000000000000000-22002i−2i00000000001-10000i3−i3−ii3−300000000
χ9066-6-6-300−6i6i-3333i3−3i33i3−3i303i−3i33−33000000000000000000000000000000000000002-200−2i2i0000000000-110000i3−i3i−i3−300000000
χ9166-6-6-300−6i6i-3333i3−3i33i3−3i303i−3i33−3300000000000000000000000000000000000000-22002i−2i00000000001-10000−i3i3−ii−3300000000
χ9212-1212-12-612i−12i006-66−6i−6i6i6i0000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9312-1212-12-6−12i12i006-666i6i−6i−6i0000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-1212-6000066-663−63−63630000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-1212-6000066-6−636363−630000000000000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).