Finite Group Databasebeta

← Group #10591216

Character table — Group #10591216

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111111122222222222222224444444444444444444444444412121212121212121212121212121212121212121212121236363636
order12222222336666666666666634466666661212121212121212121212121212121244444444121212121212121212121212121212122244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ61111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1
χ71111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1
χ81111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111
χ9222222222-12222-1-1-1-12-122-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10022002200000000-1-1-1-1-1-1-1-10000
χ10222222222-12222-1-1-1-12-122-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-200-2-200000000111111110000
χ11222222222-12222-1-1-1-12-122-1-1-1-2-2-1-1-1-1-1-1-1-2-2-2-2111111111111002200-2-200000000-1-1-1-111110000
χ12222222222-12222-1-1-1-12-122-1-1-1-2-2-1-1-1-1-1-1-1-2-2-2-211111111111100-2-20022000000001111-1-1-1-10000
χ1322222222-12-1-1-1-12222-12-1-122-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122002200-1-1-1-1-1-1-1-1000000000000
χ1422222222-12-1-1-1-12222-12-1-122-122-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-200-2-20011111111000000000000
χ1522222222-12-1-1-1-12222-12-1-122-1-2-2-1-1-1-1-1-1-11111-2-2-2-2111111112200-2-200-1-1-1-11111000000000000
χ1622222222-12-1-1-1-12222-12-1-122-1-2-2-1-1-1-1-1-1-11111-2-2-2-211111111-2-20022001111-1-1-1-1000000000000
χ17222-2-2-22-22222-2-222-2-2-2-22-22-222i−2i222-2-2-2-22i2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000
χ18222-2-2-22-22222-2-222-2-2-2-22-22-22−2i2i222-2-2-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000
χ19222-2-2-22-22-122-2-2-1-111-212-2-11-12i−2i-1-1-111112i2i−2i−2i−i−iii−i−i−i−iiiii000000000000000033−3−3−i3−i3i3i30000
χ20222-2-2-22-22-122-2-2-1-111-212-2-11-12i−2i-1-1-111112i2i−2i−2i−i−iii−i−i−i−iiiii0000000000000000−3−333i3i3−i3−i30000
χ21222-2-2-22-22-122-2-2-1-111-212-2-11-1−2i2i-1-1-11111−2i−2i2i2iii−i−iiiii−i−i−i−i000000000000000033−3−3i3i3−i3−i30000
χ22222-2-2-22-22-122-2-2-1-111-212-2-11-1−2i2i-1-1-11111−2i−2i2i2iii−i−iiiii−i−i−i−i0000000000000000−3−333−i3−i3i3i30000
χ23222-2-2-22-2-12-1-11122-2-21-2-112-2-12i−2i-1-1-11111−i−iii2i2i−2i−2i−i−i−i−iiiii0000000033−3−3−i3−i3i3i3000000000000
χ24222-2-2-22-2-12-1-11122-2-21-2-112-2-12i−2i-1-1-11111−i−iii2i2i−2i−2i−i−i−i−iiiii00000000−3−333i3i3−i3−i3000000000000
χ25222-2-2-22-2-12-1-11122-2-21-2-112-2-1−2i2i-1-1-11111ii−i−i−2i−2i2i2iiiii−i−i−i−i0000000033−3−3i3i3−i3−i3000000000000
χ26222-2-2-22-2-12-1-11122-2-21-2-112-2-1−2i2i-1-1-11111ii−i−i−2i−2i2i2iiiii−i−i−i−i00000000−3−333−i3−i3i3i3000000000000
χ2722-222-2-2-2222-22-22-2-2-222-2-2-222002-2-22-2-2200000000000000002i−2i0000002i−2i2i−2i0000000000000000
χ2822-222-2-2-2222-22-22-2-2-222-2-2-222002-2-22-2-220000000000000000−2i2i000000−2i2i−2i2i0000000000000000
χ2922-222-2-2-2-12-11-112-2-2-2-1211-22-100-111-111-1−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i32i−2i000000−ii−ii3−33−3000000000000
χ3022-222-2-2-2-12-11-112-2-2-2-1211-22-100-111-111-1−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i3−2i2i000000i−ii−i−33−33000000000000
χ3122-222-2-2-2-12-11-112-2-2-2-1211-22-100-111-111-1i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i32i−2i000000−ii−ii−33−33000000000000
χ3222-222-2-2-2-12-11-112-2-2-2-1211-22-100-111-111-1i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i3−2i2i000000i−ii−i3−33−3000000000000
χ3322-2-2-22-22222-2-222-222-2-2-22-2-22002-2-2-222-2000000000000000000002i−2i0000002i−2i−2i2i000000000000
χ3422-2-2-22-22222-2-222-222-2-2-22-2-22002-2-2-222-200000000000000000000−2i2i000000−2i2i2i−2i000000000000
χ3522-2-2-22-22-12-111-12-2221-21-1-2-2-100-1111-1-113−3−33000033−3−3−3−33300002i−2i00i3−i3−i3i3−iii−i000000000000
χ3622-2-2-22-22-12-111-12-2221-21-1-2-2-100-1111-1-113−3−33000033−3−3−3−3330000−2i2i00−i3i3i3−i3i−i−ii000000000000
χ3722-2-2-22-22-12-111-12-2221-21-1-2-2-100-1111-1-11−333−30000−3−33333−3−300002i−2i00−i3i3i3−i3−iii−i000000000000
χ3822-2-2-22-22-12-111-12-2221-21-1-2-2-100-1111-1-11−333−30000−3−33333−3−30000−2i2i00i3−i3−i3i3i−i−ii000000000000
χ392-222-22-2-222-22-2-2-222-222-22-2-2200-22-2-22-220000000000000000002i−2i0000000000002i−2i2i−2i00000000
χ402-222-22-2-222-22-2-2-222-222-22-2-2200-22-2-22-22000000000000000000−2i2i000000000000−2i2i−2i2i00000000
χ412-222-22-2-22-1-22-2-21-1-112-1-2211-1001-111-11-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3002i−2i000000000000−ii−ii3−33−30000
χ422-222-22-2-22-1-22-2-21-1-112-1-2211-1001-111-11-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i300−2i2i000000000000i−ii−i−33−330000
χ432-222-22-2-22-1-22-2-21-1-112-1-2211-1001-111-11-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3002i−2i000000000000−ii−ii−33−330000
χ442-222-22-2-22-1-22-2-21-1-112-1-2211-1001-111-11-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i300−2i2i000000000000i−ii−i3−33−30000
χ452-22-22-2-2222-2222-22-22-2-2-2-2-22200-22-22-22-200000000000000000000002i−2i0000000000002i−2i−2i2i0000
χ462-22-22-2-2222-2222-22-22-2-2-2-2-22200-22-22-22-20000000000000000000000−2i2i000000000000−2i2i2i−2i0000
χ472-22-22-2-222-1-22221-11-1-21-2-21-1-1001-11-11-1100003−3−333−33−3−33−330000002i−2i00000000i3−i3−i3i3−iii−i0000
χ482-22-22-2-222-1-22221-11-1-21-2-21-1-1001-11-11-1100003−3−333−33−3−33−33000000−2i2i00000000−i3i3i3−i3i−i−ii0000
χ492-22-22-2-222-1-22221-11-1-21-2-21-1-1001-11-11-110000−333−3−33−333−33−30000002i−2i00000000−i3i3i3−i3−iii−i0000
χ502-22-22-2-222-1-22221-11-1-21-2-21-1-1001-11-11-110000−333−3−33−333−33−3000000−2i2i00000000i3−i3−i3i3i−i−ii0000
χ512-2-22-2-22222-2-2-22-2-2-22222-22-2200-2-22-2-2220000000000000000000000000000000000000000002-2
χ522-2-22-2-22222-2-2-22-2-2-22222-22-2200-2-22-2-222000000000000000000000000000000000000000000-22
χ532-2-2-2222-222-2-22-2-2-22-2-2-22222200-2-2222-2-200000000000000000000000000000000000000002-200
χ542-2-2-2222-222-2-22-2-2-22-2-2-22222200-2-2222-2-20000000000000000000000000000000000000000-2200
χ5544444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21441111111-2-2-2-2-2-2-2-2111111110000000000000000000000000000
χ5644444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-4-4111111122222222-1-1-1-1-1-1-1-10000000000000000000000000000
χ57444-4-4-44-4-2-2-2-222-2-22222-22-2214i−4i111-1-1-1-1−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−i0000000000000000000000000000
χ58444-4-4-44-4-2-2-2-222-2-22222-22-221−4i4i111-1-1-1-12i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii0000000000000000000000000000
χ5944-444-4-4-44-24-44-4-22224-2-4-42-2-200-222-222-200000000000000000000000000000000000000000000
χ6044-444-4-4-4-2-2-22-22-2222-2-2222-21001-1-11-1-11−2i32i3−2i32i30000i3i3−i3−i3i3i3−i3−i30000000000000000000000000000
χ6144-444-4-4-4-2-2-22-22-2222-2-2222-21001-1-11-1-112i3−2i32i3−2i30000−i3−i3i3i3−i3−i3i3i30000000000000000000000000000
χ6244-4-4-44-444-24-4-44-22-2-2-42-4422-200-2222-2-2200000000000000000000000000000000000000000000
χ6344-4-4-44-44-2-2-222-2-22-2-2222-2221001-1-1-111-123−23−23230000−3−33333−3−30000000000000000000000000000
χ6444-4-4-44-44-2-2-222-2-22-2-2222-2221001-1-1-111-1−232323−23000033−3−3−3−3330000000000000000000000000000
χ654-444-44-4-4-242-222-444-4-242-2-4-4-2002-222-22-200000000000000000000000000000000000000000000
χ664-444-44-4-4-2-22-2222-2-22-2-22-222100-11-1-11-110000−2i32i3−2i32i3i3−i3i3−i3i3−i3i3−i30000000000000000000000000000
χ674-444-44-4-4-2-22-2222-2-22-2-22-222100-11-1-11-1100002i3−2i32i3−2i3−i3i3−i3i3−i3i3−i3i30000000000000000000000000000
χ684-44-44-4-44-242-2-2-2-44-442-422-44-2002-22-22-2200000000000000000000000000000000000000000000
χ694-44-44-4-44-2-22-2-2-22-22-222222-2100-11-11-11-1000023−23−2323−33−333−33−30000000000000000000000000000
χ704-44-44-4-44-2-22-2-2-22-22-222222-2100-11-11-11-10000−232323−233−33−3−33−330000000000000000000000000000
χ714-4-44-4-4444-2-4-4-44222-24-24-4-22-20022-222-2-200000000000000000000000000000000000000000000
χ724-4-44-4-444-24222-2-4-4-44-24-224-4-20022-222-2-200000000000000000000000000000000000000000000
χ734-4-44-4-444-2-2222-2222-2-2-2-22-22100-1-11-1-111000000003-3-333-3-330000000000000000000000000000
χ744-4-44-4-444-2-2222-2222-2-2-2-22-22100-1-11-1-11100000000-333-3-333-30000000000000000000000000000
χ754-4-4-4444-44-2-4-44-422-22-4244-2-2-20022-2-2-22200000000000000000000000000000000000000000000
χ764-4-4-4444-4-2422-22-4-44-42-4-2-244-20022-2-2-22200000000000000000000000000000000000000000000
χ774-4-4-4444-4-2-222-2222-2222-2-2-2-2100-1-1111-1-1000000003i−3i−3i3i−3i3i3i−3i0000000000000000000000000000
χ784-4-4-4444-4-2-222-2222-2222-2-2-2-2100-1-1111-1-100000000−3i3i3i−3i3i−3i−3i3i0000000000000000000000000000

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