Finite Group Databasebeta

← Group #10591268

Character table — Group #10591268

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222222244444444444444444444444444666666661212121212121212121212121212121212121212181818183636
order12222222336666666666666634466666661212121212121212121212121212121244444444444412121212121212121212121212121212444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
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
χ51111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ71111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ81111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1
χ911-1-11-11-111111-1-1-1-1-1-111-1-1111-111-1-1-1-1111-1-111-1-11111-1-1-1-111-1-1ii−i−i1-1i−i11-1-1ii−i−iii−i−i11-1-1ii−i−ii−i
χ1011-1-11-11-111111-1-1-1-1-1-111-1-1111-111-1-1-1-1111-1-111-1-11111-1-1-1-111-1-1−i−iii1-1−ii11-1-1−i−iii−i−iii11-1-1−i−iii−ii
χ1111-1-11-11-111111-1-1-1-1-1-111-1-1111-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-111ii−i−i-11i−i-1-111ii−i−iii−i−i-1-111−i−iii−ii
χ1211-1-11-11-111111-1-1-1-1-1-111-1-1111-111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-111−i−iii-11−ii-1-111−i−iii−i−iii-1-111ii−i−ii−i
χ1311-1-11-11-111111-1-1-1-1-1-111-1-111-1111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-1ii−i−i-11−ii11-1-1ii−i−i−i−iii-1-111ii−i−i−ii
χ1411-1-11-11-111111-1-1-1-1-1-111-1-111-1111-1-1-1-11-1-111-1-111-1-1-1-1111111-1-1−i−iii-11i−i11-1-1−i−iiiii−i−i-1-111−i−iiii−i
χ1511-1-11-11-111111-1-1-1-1-1-111-1-111-1111-1-1-1-11-1-111-1-111-1-1-1-11111-1-111ii−i−i1-1−ii-1-111ii−i−i−i−iii11-1-1−i−iiii−i
χ1611-1-11-11-111111-1-1-1-1-1-111-1-111-1111-1-1-1-11-1-111-1-111-1-1-1-11111-1-111−i−iii1-1i−i-1-111−i−iiiii−i−i11-1-1ii−i−i−ii
χ17222222222-122-122-1-1-1-12-122-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1222200002200-1-1-1-100000000-1-1-1-1000000
χ18222222222-122-122-1-1-1-12-122-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-2001111000000001111000000
χ19222222222-122-122-1-1-1-12-122-1-1-2-2-1-1-1-1-1-1-1-2-2-2-211111111111122220000-2-200-1-1-1-1000000001111000000
χ20222222222-122-122-1-1-1-12-122-1-1-2-2-1-1-1-1-1-1-1-2-2-2-2111111111111-2-2-2-200002200111100000000-1-1-1-1000000
χ2122222222-12-1-12-1-12222-12-1-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000222200220000-1-1-1-1-1-1-1-10000000000
χ2222222222-12-1-12-1-12222-12-1-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-2-2-200-2-20000111111110000000000
χ2322222222-12-1-12-1-12222-12-1-12-1-2-2-1-1-1-1-1-1-11111-2-2-2-2111111110000222200-2-20000-1-1-1-111110000000000
χ2422222222-12-1-12-1-12222-12-1-12-1-2-2-1-1-1-1-1-1-11111-2-2-2-2111111110000-2-2-2-2002200001111-1-1-1-10000000000
χ25222-2-22-2-2222-222-222-2-2-2-22-2-22002-222-2-2-2000000000000000000002-22-2000000002-22-200000000000000
χ26222-2-22-2-2222-222-222-2-2-2-22-2-22002-222-2-2-200000000000000000000-22-2200000000-22-2200000000000000
χ27222-2-22-2-2-12-112-1122-2-21-2-11-2-100-11-1-11113−33−3000033−3−333−3−300002-22-200000000-11-113−33−30000000000
χ28222-2-22-2-2-12-112-1122-2-21-2-11-2-100-11-1-11113−33−3000033−3−333−3−30000-22-22000000001-11-1−33−330000000000
χ29222-2-22-2-2-12-112-1122-2-21-2-11-2-100-11-1-1111−33−330000−3−333−3−33300002-22-200000000-11-11−33−330000000000
χ30222-2-22-2-2-12-112-1122-2-21-2-11-2-100-11-1-1111−33−330000−3−333−3−3330000-22-22000000001-11-13−33−30000000000
χ3122-22-2-2-22222-22-22-2-222-2-2-22-22002-2-2-222-2000000000000000000002i−2i−2i2i000000002i−2i−2i2i00000000000000
χ3222-22-2-2-22222-22-22-2-222-2-2-22-22002-2-2-222-200000000000000000000−2i2i2i−2i00000000−2i2i2i−2i00000000000000
χ3322-22-2-2-22-12-1121-1-2-2221-21-1-2-100-1111-1-113−3−33000033−3−3−3−33300002i−2i−2i2i00000000−iii−ii3−i3−i3i30000000000
χ3422-22-2-2-22-12-1121-1-2-2221-21-1-2-100-1111-1-113−3−33000033−3−3−3−3330000−2i2i2i−2i00000000i−i−ii−i3i3i3−i30000000000
χ3522-22-2-2-22-12-1121-1-2-2221-21-1-2-100-1111-1-11−333−30000−3−33333−3−300002i−2i−2i2i00000000−iii−i−i3i3i3−i30000000000
χ3622-22-2-2-22-12-1121-1-2-2221-21-1-2-100-1111-1-11−333−30000−3−33333−3−30000−2i2i2i−2i00000000i−i−iii3−i3−i3i30000000000
χ3722-2-22-22-22-122-1-2-211112-1-2-2-1-12-2-1-11111-122-2-2-1-111-1-1-1-1111122-2-200002-200-1-11100000000-1-111000000
χ3822-2-22-22-22-122-1-2-211112-1-2-2-1-12-2-1-11111-122-2-2-1-111-1-1-1-11111-2-2220000-220011-1-10000000011-1-1000000
χ3922-2-22-22-22-122-1-2-211112-1-2-2-1-1-22-1-11111-1-2-22211-1-11111-1-1-1-122-2-20000-2200-1-1110000000011-1-1000000
χ4022-2-22-22-22-122-1-2-211112-1-2-2-1-1-22-1-11111-1-2-22211-1-11111-1-1-1-1-2-22200002-20011-1-100000000-1-111000000
χ4122-2-22-22-2-12-1-1211-2-2-2-2-12112-12-2-1-11111-1-1-11122-2-2-1-1-1-1111100002i2i−2i−2i002i−2i0000−i−iii−i−iii0000000000
χ4222-2-22-22-2-12-1-1211-2-2-2-2-12112-12-2-1-11111-1-1-11122-2-2-1-1-1-111110000−2i−2i2i2i00−2i2i0000ii−i−iii−i−i0000000000
χ4322-2-22-22-2-12-1-1211-2-2-2-2-12112-1-22-1-11111-111-1-1-2-2221111-1-1-1-100002i2i−2i−2i00−2i2i0000−i−iiiii−i−i0000000000
χ4422-2-22-22-2-12-1-1211-2-2-2-2-12112-1-22-1-11111-111-1-1-2-2221111-1-1-1-10000−2i−2i2i2i002i−2i0000ii−i−i−i−iii0000000000
χ452-2222-2-2-222-22-2222-22-2-22-2-2-2200-222-22-2-200000000000000002-22-2000000002-22-2000000000000000000
χ462-2222-2-2-222-22-2222-22-2-22-2-2-2200-222-22-2-20000000000000000-22-2200000000-22-22000000000000000000
χ472-2222-2-2-22-1-22122-11-11-2-1-2-21-1001-1-11-11100003−33−33−33−33−33−32-22-200000000-11-11000000003−33−3000000
χ482-2222-2-2-22-1-22122-11-11-2-1-2-21-1001-1-11-11100003−33−33−33−33−33−3-22-22000000001-11-100000000−33−33000000
χ492-2222-2-2-22-1-22122-11-11-2-1-2-21-1001-1-11-1110000−33−33−33−33−33−332-22-200000000-11-1100000000−33−33000000
χ502-2222-2-2-22-1-22122-11-11-2-1-2-21-1001-1-11-1110000−33−33−33−33−33−33-22-22000000001-11-1000000003−33−3000000
χ512-22-2-2-22222-2-2-22-22-2-222-2-222200-2-22-2-222000000000000000000000000000000000000000000002-22-200
χ522-22-2-2-22222-2-2-22-22-2-222-2-222200-2-22-2-22200000000000000000000000000000000000000000000-22-2200
χ532-2-22-222-222-2-2-2-22-222-22-22-22200-2-2-222-22000000000000000000000000000000000000000000002i−2i−2i2i00
χ542-2-22-222-222-2-2-2-22-222-22-22-22200-2-2-222-2200000000000000000000000000000000000000000000−2i2i2i−2i00
χ552-2-2-222-2222-22-2-2-2-22-22-2222-2200-22-22-22-200000000000000002-2-22000000002-2-22000000000000000000
χ562-2-2-222-2222-22-2-2-2-22-22-2222-2200-22-22-22-20000000000000000-222-200000000-222-2000000000000000000
χ572-2-2-222-222-1-221-2-21-11-1-2-1221-1001-11-11-1100003−3−333−33−3−33−332-2-2200000000-111-1000000003−3−33000000
χ582-2-2-222-222-1-221-2-21-11-1-2-1221-1001-11-11-1100003−3−333−33−3−33−33-222-2000000001-1-1100000000−333−3000000
χ592-2-2-222-222-1-221-2-21-11-1-2-1221-1001-11-11-110000−333−3−33−333−33−32-2-2200000000-111-100000000−333−3000000
χ602-2-2-222-222-1-221-2-21-11-1-2-1221-1001-11-11-110000−333−3−33−333−33−3-222-2000000001-1-11000000003−3−33000000
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
χ63444-4-44-4-44-24-4-24-4-2-222-424-42-200-22-2-222200000000000000000000000000000000000000000000000000
χ64444-4-44-4-4-2-2-22-2-22-2-22222-2221001-111-1-1-123−2323−230000−3−333−3−3330000000000000000000000000000000000
χ65444-4-44-4-4-2-2-22-2-22-2-22222-2221001-111-1-1-1−2323−2323000033−3−333−3−30000000000000000000000000000000000
χ6644-44-4-4-444-24-4-2-4422-2-2-42-442-200-2222-2-2200000000000000000000000000000000000000000000000000
χ6744-44-4-4-44-2-2-22-22-222-2-2222-221001-1-1-111-123−23−23230000−3−33333−3−30000000000000000000000000000000000
χ6844-44-4-4-44-2-2-22-22-222-2-2222-221001-1-1-111-1−232323−23000033−3−3−3−3330000000000000000000000000000000000
χ6944-4-44-44-4-2-2-2-2-2222222-2-222-214-411-1-1-1-11-2-222-2-2221111-1-1-1-10000000000000000000000000000000000
χ7044-4-44-44-4-2-2-2-2-2222222-2-222-21-4411-1-1-1-1122-2-222-2-2-1-1-1-111110000000000000000000000000000000000
χ714-4444-4-4-4-242-2-4-2-24-44-42422-4-2002-2-22-22200000000000000000000000000000000000000000000000000
χ724-4444-4-4-4-2-22-22-2-2-22-222-2222100-111-11-1-1000023−2323−23−33−33−33−330000000000000000000000000000000000
χ734-4444-4-4-4-2-22-22-2-2-22-222-2222100-111-11-1-10000−2323−23233−33−33−33−30000000000000000000000000000000000
χ744-44-4-4-4444-2-4-424-4-222-242-44-2-20022-222-2-200000000000000000000000000000000000000000000000000
χ754-44-4-4-444-2422-4-224-4-44-2-42-24-20022-222-2-200000000000000000000000000000000000000000000000000
χ764-44-4-4-444-2-2222-22-222-2-222-2-2100-1-11-1-111000000003-3-333-3-330000000000000000000000000000000000
χ774-44-4-4-444-2-2222-22-222-2-222-2-2100-1-11-1-11100000000-333-3-333-30000000000000000000000000000000000
χ784-4-44-444-44-2-4-42-442-2-22424-4-2-200222-2-22-200000000000000000000000000000000000000000000000000
χ794-4-44-444-4-2422-42-2-444-4-2-4-224-200222-2-22-200000000000000000000000000000000000000000000000000
χ804-4-44-444-4-2-22222-22-2-22-22-22-2100-1-1-111-11000000003-3-33-333-30000000000000000000000000000000000
χ814-4-44-444-4-2-22222-22-2-22-22-22-2100-1-1-111-1100000000-333-33-3-330000000000000000000000000000000000
χ824-4-4-444-44-242-2-422-44-4424-2-2-4-2002-22-22-2200000000000000000000000000000000000000000000000000
χ834-4-4-444-44-2-22-22222-22-22-2-2-22100-11-11-11-1000023−23−2323−33−333−33−30000000000000000000000000000000000
χ844-4-4-444-44-2-22-22222-22-22-2-2-22100-11-11-11-10000−232323−233−33−3−33−330000000000000000000000000000000000

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