Finite Group Databasebeta

← Group #10591273

Character table — Group #10591273

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222222244444444444444444444444444666666661212121212121212121212121212121212121212181818183636
order12222222336666666666666634466666661212121212121212121212121212121244444444444412121212121212121212121212121212444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ61111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1
χ9111-1-1-1-11111111-1-1-1-111-1-1-1-111-111-1-1-1-111111-1-1-1-11111-1-1-1-1ii−i−iii−i−ii−ii−iii−i−iii−i−iii−i−iii−i−i11-1-11-1
χ10111-1-1-1-11111111-1-1-1-111-1-1-1-111-111-1-1-1-111111-1-1-1-11111-1-1-1-1ii−i−i−i−iiii−i−iiii−i−iii−i−i−i−iii−i−iii-1-111-11
χ11111-1-1-1-11111111-1-1-1-111-1-1-1-111-111-1-1-1-111111-1-1-1-11111-1-1-1-1−i−iiiii−i−i−iii−i−i−iii−i−iiiii−i−iii−i−i-1-111-11
χ12111-1-1-1-11111111-1-1-1-111-1-1-1-111-111-1-1-1-111111-1-1-1-11111-1-1-1-1−i−iii−i−iii−ii−ii−i−iii−i−iii−i−iii−i−iii11-1-11-1
χ13111-1-1-1-11111111-1-1-1-111-1-1-1-11-1111-1-1-1-11-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−ii−iiii−i−i−i−iiiii−i−i−i−iii11-1-1-11
χ14111-1-1-1-11111111-1-1-1-111-1-1-1-11-1111-1-1-1-11-1-1-1-11111-1-1-1-11111ii−i−i−i−iii−iii−iii−i−i−i−iii−i−iiiii−i−i-1-1111-1
χ15111-1-1-1-11111111-1-1-1-111-1-1-1-11-1111-1-1-1-11-1-1-1-11111-1-1-1-11111−i−iiiii−i−ii−i−ii−i−iiiii−i−iii−i−i−i−iii-1-1111-1
χ16111-1-1-1-11111111-1-1-1-111-1-1-1-11-1111-1-1-1-11-1-1-1-11111-1-1-1-11111−i−iii−i−iiii−ii−i−i−iiiii−i−i−i−iiiii−i−i11-1-1-11
χ17222222222-122-1-122-1-12-122-1-1-122-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-100002222002200000000-1-1-1-1-1-1-1-1000000
χ18222222222-122-1-122-1-12-122-1-1-122-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-10000-2-2-2-200-2-20000000011111111000000
χ19222222222-122-1-122-1-12-122-1-1-1-2-2-1-1-1-1-1-1-1-2-211-2-211111111110000222200-2-200000000-1-1-1-11111000000
χ20222222222-122-1-122-1-12-122-1-1-1-2-2-1-1-1-1-1-1-1-2-211-2-211111111110000-2-2-2-20022000000001111-1-1-1-1000000
χ2122222222-12-1-122-1-122-12-1-122-122-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1222200002200-1-1-1-1-1-1-1-100000000000000
χ2222222222-12-1-122-1-122-12-1-122-122-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-2-2-2-20000-2-2001111111100000000000000
χ2322222222-12-1-122-1-122-12-1-122-1-2-2-1-1-1-1-1-1-111-2-211-2-21111111122220000-2-200-1-1-1-1111100000000000000
χ2422222222-12-1-122-1-122-12-1-122-1-2-2-1-1-1-1-1-1-111-2-211-2-211111111-2-2-2-2000022001111-1-1-1-100000000000000
χ25222-2-2-2-222-122-1-1-2-2112-1-2-211-12-2-1-11111-122-1-1-2-211-1-1-1-1111100002i2i−2i−2i002i−2i00000000−i−iii−i−iii000000
χ26222-2-2-2-222-122-1-1-2-2112-1-2-211-12-2-1-11111-122-1-1-2-211-1-1-1-111110000−2i−2i2i2i00−2i2i00000000ii−i−iii−i−i000000
χ27222-2-2-2-222-122-1-1-2-2112-1-2-211-1-22-1-11111-1-2-21122-1-11111-1-1-1-100002i2i−2i−2i00−2i2i00000000−i−iiiii−i−i000000
χ28222-2-2-2-222-122-1-1-2-2112-1-2-211-1-22-1-11111-1-2-21122-1-11111-1-1-1-10000−2i−2i2i2i002i−2i00000000ii−i−i−i−iii000000
χ29222-2-2-2-22-12-1-12211-2-2-1211-2-2-12-2-1-11111-1-1-12211-2-2-1-1-1-111112i2i−2i−2i00002i−2i00−i−iii−i−iii00000000000000
χ30222-2-2-2-22-12-1-12211-2-2-1211-2-2-12-2-1-11111-1-1-12211-2-2-1-1-1-11111−2i−2i2i2i0000−2i2i00ii−i−iii−i−i00000000000000
χ31222-2-2-2-22-12-1-12211-2-2-1211-2-2-1-22-1-11111-111-2-2-1-1221111-1-1-1-12i2i−2i−2i0000−2i2i00−i−iiiii−i−i00000000000000
χ32222-2-2-2-22-12-1-12211-2-2-1211-2-2-1-22-1-11111-111-2-2-1-1221111-1-1-1-1−2i−2i2i2i00002i−2i00ii−i−i−i−iii00000000000000
χ3322-222-2-2-2222-22-2222-2-2-2-2-22-22002-222-2-2-2000000000000000000002-22-20000000000002-22-20000000000
χ3422-222-2-2-2222-22-2222-2-2-2-2-22-22002-222-2-2-200000000000000000000-22-22000000000000-22-220000000000
χ3522-222-2-2-22-12-2-1122-11-21-2-2-11-100-11-1-1111003−3003−333−3−333−3−300002-22-2000000000000-11-113−33−3000000
χ3622-222-2-2-22-12-2-1122-11-21-2-2-11-100-11-1-1111003−3003−333−3−333−3−30000-22-220000000000001-11-1−33−33000000
χ3722-222-2-2-22-12-2-1122-11-21-2-2-11-100-11-1-111100−3300−33−3−333−3−33300002-22-2000000000000-11-11−33−33000000
χ3822-222-2-2-22-12-2-1122-11-21-2-2-11-100-11-1-111100−3300−33−3−333−3−3330000-22-220000000000001-11-13−33−3000000
χ3922-2-2-222-2222-22-2-2-2-22-2-222-222002-2-2-222-2000000000000000000002i−2i−2i2i0000000000002i−2i−2i2i0000000000
χ4022-2-2-222-2222-22-2-2-2-22-2-222-222002-2-2-222-200000000000000000000−2i2i2i−2i000000000000−2i2i2i−2i0000000000
χ4122-2-2-222-22-12-2-11-2-21-1-21221-1-100-1111-1-11003−300−3333−3−3−3−33300002i−2i−2i2i000000000000−iii−ii3−i3−i3i3000000
χ4222-2-2-222-22-12-2-11-2-21-1-21221-1-100-1111-1-11003−300−3333−3−3−3−3330000−2i2i2i−2i000000000000i−i−ii−i3i3i3−i3000000
χ4322-2-2-222-22-12-2-11-2-21-1-21221-1-100-1111-1-1100−33003−3−3−33333−3−300002i−2i−2i2i000000000000−iii−i−i3i3i3−i3000000
χ4422-2-2-222-22-12-2-11-2-21-1-21221-1-100-1111-1-1100−33003−3−3−33333−3−30000−2i2i2i−2i000000000000i−i−iii3−i3−i3i3000000
χ452-222-22-2-222-22-222-222-2-22-2-2-2200-222-22-2-200000000000000002-22-2000000002-22-2000000000000000000
χ462-222-22-2-222-22-222-222-2-22-2-2-2200-222-22-2-20000000000000000-22-2200000000-22-22000000000000000000
χ472-222-22-2-2-121-1-22-11221-2-11-2-2-1001-1-11-1113−3003−3003−33−33−33−32-22-200000000-11-113−33−300000000000000
χ482-222-22-2-2-121-1-22-11221-2-11-2-2-1001-1-11-1113−3003−3003−33−33−33−3-22-22000000001-11-1−33−3300000000000000
χ492-222-22-2-2-121-1-22-11221-2-11-2-2-1001-1-11-111−3300−3300−33−33−33−332-22-200000000-11-11−33−3300000000000000
χ502-222-22-2-2-121-1-22-11221-2-11-2-2-1001-1-11-111−3300−3300−33−33−33−33-22-22000000001-11-13−33−300000000000000
χ512-22-22-22-222-22-22-22-2-2-2-2-2222200-22-22-22-200000000000000002i−2i−2i2i000000002i−2i−2i2i000000000000000000
χ522-22-22-22-222-22-22-22-2-2-2-2-2222200-22-22-22-20000000000000000−2i2i2i−2i00000000−2i2i2i−2i000000000000000000
χ532-22-22-22-2-121-1-221-1-2-21-21-122-1001-11-11-113−300−33003−33−3−33−332i−2i−2i2i00000000−iii−ii3−i3−i3i300000000000000
χ542-22-22-22-2-121-1-221-1-2-21-21-122-1001-11-11-113−300−33003−33−3−33−33−2i2i2i−2i00000000i−i−ii−i3i3i3−i300000000000000
χ552-22-22-22-2-121-1-221-1-2-21-21-122-1001-11-11-11−33003−300−33−333−33−32i−2i−2i2i00000000−iii−i−i3i3i3−i300000000000000
χ562-22-22-22-2-121-1-221-1-2-21-21-122-1001-11-11-11−33003−300−33−333−33−3−2i2i2i−2i00000000i−i−iii3−i3−i3i300000000000000
χ572-2-22-2-22222-2-2-2-22-22-222-22-22200-2-22-2-222000000000000000000000000000000000000000000002-22-200
χ582-2-22-2-22222-2-2-2-22-22-222-22-22200-2-22-2-22200000000000000000000000000000000000000000000-22-2200
χ592-2-2-222-2222-2-2-2-2-22-22222-22-2200-2-2-222-22000000000000000000000000000000000000000000002-2-2200
χ602-2-2-222-2222-2-2-2-2-22-22222-22-2200-2-2-222-2200000000000000000000000000000000000000000000-222-200
χ6144444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21441111111-2-2-2-2-2-2-2-2111111110000000000000000000000000000000000
χ6244444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-4-4111111122222222-1-1-1-1-1-1-1-10000000000000000000000000000000000
χ63444-4-4-4-44-2-2-2-2-2-22222-2-2222214-411-1-1-1-11-2-2-2-222221111-1-1-1-10000000000000000000000000000000000
χ64444-4-4-4-44-2-2-2-2-2-22222-2-222221-4411-1-1-1-112222-2-2-2-2-1-1-1-111110000000000000000000000000000000000
χ6544-444-4-4-4-24-224-4-2-24-42-4224-4-200-22-2-222200000000000000000000000000000000000000000000000000
χ6644-444-4-4-4-2-2-22-22-2-2-222222-221001-111-1-1-10023−230023−23−3−333−3−3330000000000000000000000000000000000
χ6744-444-4-4-4-2-2-22-22-2-2-222222-221001-111-1-1-100−232300−232333−3−333−3−30000000000000000000000000000000000
χ6844-4-4-444-4-24-224-422-442-4-2-2-44-200-2222-2-2200000000000000000000000000000000000000000000000000
χ6944-4-4-444-4-2-2-22-22222-222-2-22-21001-1-1-111-10023−2300−2323−3−33333−3−30000000000000000000000000000000000
χ7044-4-4-444-4-2-2-22-22222-222-2-22-21001-1-1-111-100−23230023−2333−3−3−3−3330000000000000000000000000000000000
χ714-444-44-4-44-2-442-24-4-2-2-424-422-2002-2-22-22200000000000000000000000000000000000000000000000000
χ724-444-44-4-4-2-22-22-2-22-2-222-2222100-111-11-1-123−230023−2300−33−33−33−330000000000000000000000000000000000
χ734-444-44-4-4-2-22-22-2-22-2-222-2222100-111-11-1-1−232300−2323003−33−33−33−30000000000000000000000000000000000
χ744-44-44-44-44-2-442-2-4422-42-44-2-2-2002-22-22-2200000000000000000000000000000000000000000000000000
χ754-44-44-44-4-2-22-22-22-222222-2-2-2100-11-11-11-123−2300−232300−33−333−33−30000000000000000000000000000000000
χ764-44-44-44-4-2-22-22-22-222222-2-2-2100-11-11-11-1−23230023−23003−33−3−33−330000000000000000000000000000000000
χ774-4-44-4-4444-2-4-4224-4-224-2-442-2-20022-222-2-200000000000000000000000000000000000000000000000000
χ784-4-44-4-444-2422-4-4-224-4-242-2-44-20022-222-2-200000000000000000000000000000000000000000000000000
χ794-4-44-4-444-2-22222-22-22-2-22-22-2100-1-11-1-111000000003-3-333-3-330000000000000000000000000000000000
χ804-4-44-4-444-2-22222-22-22-2-22-22-2100-1-11-1-11100000000-333-3-333-30000000000000000000000000000000000
χ814-4-4-444-444-2-4-422-442-24-24-4-22-200222-2-22-200000000000000000000000000000000000000000000000000
χ824-4-4-444-44-2422-4-42-2-44-24-224-4-200222-2-22-200000000000000000000000000000000000000000000000000
χ834-4-4-444-44-2-222222-22-2-2-2-22-22100-1-1-111-11000000003-3-33-333-30000000000000000000000000000000000
χ844-4-4-444-44-2-222222-22-2-2-2-22-22100-1-1-111-1100000000-333-33-3-330000000000000000000000000000000000

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