Finite Group Databasebeta

← Group #10591235

Character table — Group #10591235

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222222244444444444444444444444444666666661212121212121212121212121212121212121212181818183636
order12222222336666666666666634466666661212121212121212121212121212121244444444444412121212121212121212121212121212444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
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
χ61111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111
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
χ9111-1-1-1-11111111-1-1-1-1-1-111-1-11i−i111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−i11-1-1i−i1-1ii−i−i11-1-111-1-1ii−i−iii−i−i1-1
χ10111-1-1-1-11111111-1-1-1-1-1-111-1-11i−i111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−i-1-111−ii1-1ii−i−i11-1-1-1-111−i−iii−i−iii-11
χ11111-1-1-1-11111111-1-1-1-1-1-111-1-11i−i111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i−i−iii11-1-1i−i-11−i−iii-1-11111-1-1ii−i−i−i−iii-11
χ12111-1-1-1-11111111-1-1-1-1-1-111-1-11i−i111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−i−i−iii-1-111−ii-11−i−iii-1-111-1-111−i−iiiii−i−i1-1
χ13111-1-1-1-11111111-1-1-1-1-1-111-1-11−ii111-1-1-1-1−i−iii−i−iii−i−i−i−iiiiiii−i−i11-1-1−ii-11ii−i−i-1-11111-1-1−i−iiiii−i−i-11
χ14111-1-1-1-11111111-1-1-1-1-1-111-1-11−ii111-1-1-1-1−i−iii−i−iii−i−i−i−iiiiiii−i−i-1-111i−i-11ii−i−i-1-111-1-111ii−i−i−i−iii1-1
χ15111-1-1-1-11111111-1-1-1-1-1-111-1-11−ii111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii11-1-1−ii1-1−i−iii11-1-111-1-1−i−iii−i−iii1-1
χ16111-1-1-1-11111111-1-1-1-1-1-111-1-11−ii111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii-1-111i−i1-1−i−iii11-1-1-1-111ii−i−iii−i−i-11
χ17222222222-122-1-1222-1-1-12-1-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222200000022-1-1-1-1-1-1-1-100000000000000
χ18222222222-122-1-1222-1-1-12-1-12-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2000000-2-21111111100000000000000
χ19222222222-122-1-1222-1-1-12-1-12-1-2-2-1-1-1-1-1-1-11111-2-2-2-2111111112222000000-2-2-1-1-1-1111100000000000000
χ20222222222-122-1-1222-1-1-12-1-12-1-2-2-1-1-1-1-1-1-11111-2-2-2-211111111-2-2-2-2000000221111-1-1-1-100000000000000
χ2122222222-12-1-122-1-1-1222-122-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100002222220000000000-1-1-1-1-1-1-1-1000000
χ2222222222-12-1-122-1-1-1222-122-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-2-2-2000000000011111111000000
χ2322222222-12-1-122-1-1-1222-122-1-1-2-2-1-1-1-1-1-1-1-2-2-2-211111111111100002222-2-20000000000-1-1-1-11111000000
χ2422222222-12-1-122-1-1-1222-122-1-1-2-2-1-1-1-1-1-1-1-2-2-2-21111111111110000-2-2-2-22200000000001111-1-1-1-1000000
χ25222-2-2-2-222-122-1-1-2-2-21112-11-2-12i−2i-1-1-11111−i−iii2i2i−2i−2i−i−i−i−iiiii2i2i−2i−2i0000002-2−i−iii-1-11100000000000000
χ26222-2-2-2-222-122-1-1-2-2-21112-11-2-12i−2i-1-1-11111−i−iii2i2i−2i−2i−i−i−i−iiiii−2i−2i2i2i000000-22ii−i−i11-1-100000000000000
χ27222-2-2-2-222-122-1-1-2-2-21112-11-2-1−2i2i-1-1-11111ii−i−i−2i−2i2i2iiiii−i−i−i−i2i2i−2i−2i000000-22−i−iii11-1-100000000000000
χ28222-2-2-2-222-122-1-1-2-2-21112-11-2-1−2i2i-1-1-11111ii−i−i−2i−2i2i2iiiii−i−i−i−i−2i−2i2i2i0000002-2ii−i−i-1-11100000000000000
χ29222-2-2-2-22-12-1-122111-2-2-2-12-21-12i−2i-1-1-111112i2i−2i−2i−i−iii−i−i−i−iiiii000022-2-22i−2i0000000000-1-111−i−iii000000
χ30222-2-2-2-22-12-1-122111-2-2-2-12-21-12i−2i-1-1-111112i2i−2i−2i−i−iii−i−i−i−iiiii0000-2-222−2i2i000000000011-1-1ii−i−i000000
χ31222-2-2-2-22-12-1-122111-2-2-2-12-21-1−2i2i-1-1-11111−2i−2i2i2iii−i−iiiii−i−i−i−i000022-2-2−2i2i0000000000-1-111ii−i−i000000
χ32222-2-2-2-22-12-1-122111-2-2-2-12-21-1−2i2i-1-1-11111−2i−2i2i2iii−i−iiiii−i−i−i−i0000-2-2222i−2i000000000011-1-1−i−iii000000
χ3322-222-2-2-2222-22-222-22-2-2-2-22-22002-2-222-2-200000000000000002-22-2000000002-22-2000000000000000000
χ3422-222-2-2-2222-22-222-22-2-2-2-22-22002-2-222-2-20000000000000000-22-2200000000-22-22000000000000000000
χ3522-222-2-2-22-12-2-1122-2-111-21-1-2-100-111-1-1113−33−3000033−3−333−3−32-22-200000000-11-113−33−300000000000000
χ3622-222-2-2-22-12-2-1122-2-111-21-1-2-100-111-1-1113−33−3000033−3−333−3−3-22-22000000001-11-1−33−3300000000000000
χ3722-222-2-2-22-12-2-1122-2-111-21-1-2-100-111-1-111−33−330000−3−333−3−3332-22-200000000-11-11−33−3300000000000000
χ3822-222-2-2-22-12-2-1122-2-111-21-1-2-100-111-1-111−33−330000−3−333−3−333-22-22000000001-11-13−33−300000000000000
χ3922-2-2-222-2222-22-2-2-22-222-2-2-222002-2-2-2-22200000000000000002i−2i−2i2i000000002i−2i−2i2i000000000000000000
χ4022-2-2-222-2222-22-2-2-22-222-2-2-222002-2-2-2-2220000000000000000−2i2i2i−2i00000000−2i2i2i−2i000000000000000000
χ4122-2-2-222-22-12-2-11-2-221-1-1-2112-100-11111-1-1−i3i3i3−i30000−i3−i3i3i3i3i3−i3−i32i−2i−2i2i00000000−iii−i−333−300000000000000
χ4222-2-2-222-22-12-2-11-2-221-1-1-2112-100-11111-1-1−i3i3i3−i30000−i3−i3i3i3i3i3−i3−i3−2i2i2i−2i00000000i−i−ii3−3−3300000000000000
χ4322-2-2-222-22-12-2-11-2-221-1-1-2112-100-11111-1-1i3−i3−i3i30000i3i3−i3−i3−i3−i3i3i32i−2i−2i2i00000000−iii−i3−3−3300000000000000
χ4422-2-2-222-22-12-2-11-2-221-1-1-2112-100-11111-1-1i3−i3−i3i30000i3i3−i3−i3−i3−i3i3i3−2i2i2i−2i00000000i−i−ii−333−300000000000000
χ452-222-2-22-222-22-222-2222-2-2-2-2-2200-22-22-22-2000000000000000000000000000000000000000000002-22-200
χ462-222-2-22-222-22-222-2222-2-2-2-2-2200-22-22-22-200000000000000000000000000000000000000000000-22-2200
χ472-22-222-2-222-22-22-22-2-2-22-2-222200-22-2-22-22000000000000000000000000000000000000000000002i−2i−2i2i00
χ482-22-222-2-222-22-22-22-2-2-22-2-222200-22-2-22-2200000000000000000000000000000000000000000000−2i2i2i−2i00
χ492-2-22-22-2222-2-2-2-22-2-22-2222-22200-2-222-2-22000000000000000000002-22-20000000000002-22-20000000000
χ502-2-22-22-2222-2-2-2-22-2-22-2222-22200-2-222-2-2200000000000000000000-22-22000000000000-22-220000000000
χ512-2-22-22-22-1211-2-2-1112-22-12-2-1-10011-1-111-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i300002-22-2000000000000-11-11−i3i3−i3i3000000
χ522-2-22-22-22-1211-2-2-1112-22-12-2-1-10011-1-111-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30000-22-220000000000001-11-1i3−i3i3−i3000000
χ532-2-22-22-22-1211-2-2-1112-22-12-2-1-10011-1-111-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i300002-22-2000000000000-11-11i3−i3i3−i3000000
χ542-2-22-22-22-1211-2-2-1112-22-12-2-1-10011-1-111-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30000-22-220000000000001-11-1−i3i3−i3i3000000
χ552-2-2-22-22222-2-2-2-2-222-22-2222-2200-2-22-222-2000000000000000000002-2-220000000000002-2-220000000000
χ562-2-2-22-22222-2-2-2-2-222-22-2222-2200-2-22-222-200000000000000000000-222-2000000000000-222-20000000000
χ572-2-2-22-222-1211-2-21-1-1-22-2-1221-10011-11-1-1100003−3−333−33−3−33−3300002-2-22000000000000-111-13−3−33000000
χ582-2-2-22-222-1211-2-21-1-1-22-2-1221-10011-11-1-1100003−3−333−33−3−33−330000-222-20000000000001-1-11−333−3000000
χ592-2-2-22-222-1211-2-21-1-1-22-2-1221-10011-11-1-110000−333−3−33−333−33−300002-2-22000000000000-111-1−333−3000000
χ602-2-2-22-222-1211-2-21-1-1-22-2-1221-10011-11-1-110000−333−3−33−333−33−30000-222-20000000000001-1-113−3−33000000
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
χ63444-4-4-4-44-2-2-2-2-2-2222222-2-22214i−4i111-1-1-1-1−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−i0000000000000000000000000000000000
χ64444-4-4-4-44-2-2-2-2-2-2222222-2-2221−4i4i111-1-1-1-12i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii0000000000000000000000000000000000
χ6544-444-4-4-4-24-224-4-2-224-4-42-442-200-222-2-22200000000000000000000000000000000000000000000000000
χ6644-444-4-4-4-2-2-22-22-2-22-22222-221001-1-111-1-123−2323−230000−3−333−3−3330000000000000000000000000000000000
χ6744-444-4-4-4-2-2-22-22-2-22-22222-221001-1-111-1-1−2323−2323000033−3−333−3−30000000000000000000000000000000000
χ6844-4-4-444-4-24-224-422-2-4442-4-4-2-200-22222-2-200000000000000000000000000000000000000000000000000
χ6944-4-4-444-4-2-2-22-2222-22-2-2222-21001-1-1-1-111−2i32i32i3−2i30000i3i3−i3−i3−i3−i3i3i30000000000000000000000000000000000
χ7044-4-4-444-4-2-2-22-2222-22-2-2222-21001-1-1-1-1112i3−2i3−2i32i30000−i3−i3i3i3i3i3−i3−i30000000000000000000000000000000000
χ714-444-4-44-44-2-442-24-44-2-22-422-4-2002-22-22-2200000000000000000000000000000000000000000000000000
χ724-444-4-44-4-242-2-44-22-244-42-4-42-2002-22-22-2200000000000000000000000000000000000000000000000000
χ734-444-4-44-4-2-22-22-2-22-2-2-222222100-11-11-11-1000000003i−3i−3i3i3i−3i−3i3i0000000000000000000000000000000000
χ744-444-4-44-4-2-22-22-2-22-2-2-222222100-11-11-11-100000000−3i3i3i−3i−3i3i3i−3i0000000000000000000000000000000000
χ754-44-444-4-44-2-442-2-44-422-2-42-24-2002-222-22-200000000000000000000000000000000000000000000000000
χ764-44-444-4-4-242-2-442-22-4-442-44-2-2002-222-22-200000000000000000000000000000000000000000000000000
χ774-44-444-4-4-2-22-22-22-2222-222-2-2100-11-1-11-11000000003-3-33-333-30000000000000000000000000000000000
χ784-44-444-4-4-2-22-22-22-2222-222-2-2100-11-1-11-1100000000-333-33-3-330000000000000000000000000000000000
χ794-4-44-44-444-2-4-4224-4-4-22-24-224-20022-2-222-200000000000000000000000000000000000000000000000000
χ804-4-44-44-44-2-22222-222-22-2-2-22-2100-1-111-1-110000−2i32i3−2i32i3i3−i3i3−i3i3−i3i3−i30000000000000000000000000000000000
χ814-4-44-44-44-2-22222-222-22-2-2-22-2100-1-111-1-1100002i3−2i32i3−2i3−i3i3−i3i3−i3i3−i3i30000000000000000000000000000000000
χ824-4-4-44-4444-2-4-422-4442-224-2-2-4-20022-22-2-2200000000000000000000000000000000000000000000000000
χ834-4-4-44-444-2-222222-2-22-22-2-2-22100-1-11-111-1000023−23−2323−33−333−33−30000000000000000000000000000000000
χ844-4-4-44-444-2-222222-2-22-22-2-2-22100-1-11-111-10000−232323−233−33−3−33−330000000000000000000000000000000000

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