Finite Group Databasebeta

← Group #13140007

Character table — Group #13140007

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order1222222236666666441212121233666666666666663666666612121212121212121212121212121212444444444444121212121212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ922222222222222222222222-12222-1-1-1-12-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000022220000000000000000-1-1-1-1-1-1-1-1
χ1022222222222222222222222-12222-1-1-1-12-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-2000000000000000011111111
χ112222222222222222222222-12-1-1-1-12222-12-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100002222000000000000-1-1-1-1-1-1-1-100000000
χ122222222222222222222222-12-1-1-1-12222-12-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-2-2-20000000000001111111100000000
χ132222222222222222-2-2-2-2-2-22-12222-1-1-1-12-122-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000000022-2-20000000000000000-1-1-1-11111
χ142222222222222222-2-2-2-2-2-22-12222-1-1-1-12-122-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111111100000000-2-22200000000000000001111-1-1-1-1
χ152222222222222222-2-2-2-2-2-2-12-1-1-1-12222-12-1-122-1-1-1-1-1-1-1-11111-2-2-2-211111111000022-2-2000000000000-1-1-1-1111100000000
χ162222222222222222-2-2-2-2-2-2-12-1-1-1-12222-12-1-122-1-1-1-1-1-1-1-11111-2-2-2-2111111110000-2-2220000000000001111-1-1-1-100000000
χ172222-2-2-2-2222-2-22-2-2000000222-2-2-22-2-2-2222-22-2222-2-2-2-220000000000000000002i−2i0000000000002i2i−2i−2i0000000000000000
χ182222-2-2-2-2222-2-22-2-2000000222-2-2-22-2-2-2222-22-2222-2-2-2-22000000000000000000−2i2i000000000000−2i−2i2i2i0000000000000000
χ1922-2-222-2-22-2-22-222-200000022-222-2-22-2-222-2-2-222-2-222-2-22000000000000000000002i−2i000000000000002i2i−2i−2i000000000000
χ2022-2-222-2-22-2-22-222-200000022-222-2-22-2-222-2-2-222-2-222-2-2200000000000000000000−2i2i00000000000000−2i−2i2i2i000000000000
χ2122-2-222-2-22-2-22-222-2000000-121-1-11-22-2-2-1211-22-111-1-111-1−i3−i3i3i30000−i3−i3−i3−i3i3i3i3i300002i−2i00000000000000−i−iii33−3−300000000
χ2222-2-222-2-22-2-22-222-2000000-121-1-11-22-2-2-1211-22-111-1-111-1−i3−i3i3i30000−i3−i3−i3−i3i3i3i3i30000−2i2i00000000000000ii−i−i−3−33300000000
χ2322-2-222-2-22-2-22-222-2000000-121-1-11-22-2-2-1211-22-111-1-111-1i3i3−i3−i30000i3i3i3i3−i3−i3−i3−i300002i−2i00000000000000−i−iii−3−33300000000
χ2422-2-222-2-22-2-22-222-2000000-121-1-11-22-2-2-1211-22-111-1-111-1i3i3−i3−i30000i3i3i3i3−i3−i3−i3−i30000−2i2i00000000000000ii−i−i33−3−300000000
χ2522-2-2-2-2222-2-2-222-2200000022-2-2-22-2-22222-22-2-22-2-2-2-2222000000000000000000000000002i−2i000000000000000000002i2i−2i−2i
χ2622-2-2-2-2222-2-2-222-2200000022-2-2-22-2-22222-22-2-22-2-2-2-222200000000000000000000000000−2i2i00000000000000000000−2i−2i2i2i
χ2722-2-2-2-2222-2-2-222-220000002-1-2-2-2211-1-12-1-2211-11111-1-1-10000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300000000002i−2i000000000000000033−3−3−i−iii
χ2822-2-2-2-2222-2-2-222-220000002-1-2-2-2211-1-12-1-2211-11111-1-1-10000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000−2i2i0000000000000000−3−333ii−i−i
χ2922-2-2-2-2222-2-2-222-220000002-1-2-2-2211-1-12-1-2211-11111-1-1-10000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300000000002i−2i0000000000000000−3−333−i−iii
χ3022-2-2-2-2222-2-2-222-220000002-1-2-2-2211-1-12-1-2211-11111-1-1-10000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000−2i2i000000000000000033−3−3ii−i−i
χ312-22-22-22-222-222-2-2-200000022-22-2-22-22-2-2-222-2222-22-22-2-20000000000000000000000002i−2i0000000000000000002i−2i2i−2i0000
χ322-22-22-22-222-222-2-2-200000022-22-2-22-22-2-2-222-2222-22-22-2-2000000000000000000000000−2i2i000000000000000000−2i2i−2i2i0000
χ332-22-22-22-222-222-2-2-20000002-1-22-2-2-11-11-21221-1-1-11-11-11100003−33−33−33−33−33−3000000002i−2i000000000000000000−ii−ii−i3i3−i3i3
χ342-22-22-22-222-222-2-2-20000002-1-22-2-2-11-11-21221-1-1-11-11-11100003−33−33−33−33−33−300000000−2i2i000000000000000000i−ii−ii3−i3i3−i3
χ352-22-22-22-222-222-2-2-20000002-1-22-2-2-11-11-21221-1-1-11-11-1110000−33−33−33−33−33−33000000002i−2i000000000000000000−ii−iii3−i3i3−i3
χ362-22-22-22-222-222-2-2-20000002-1-22-2-2-11-11-21221-1-1-11-11-1110000−33−33−33−33−33−3300000000−2i2i000000000000000000i−ii−i−i3i3−i3i3
χ372-22-2-22-2222-2-2-2-22200000022-2-22222-22-2-22-2-2-222-2-22-22-200000000000000000000002i−2i00000000000000002i−2i2i−2i00000000
χ382-22-2-22-2222-2-2-2-22200000022-2-22222-22-2-22-2-2-222-2-22-22-20000000000000000000000−2i2i0000000000000000−2i2i−2i2i00000000
χ392-22-2-22-2222-2-2-2-222000000-1211-1-122-221-2-11-2-2-1-111-11-113−33−300003−3−33−333−30000002i−2i000000000000−i3i3−i3i3−ii−ii00000000
χ402-22-2-22-2222-2-2-2-222000000-1211-1-122-221-2-11-2-2-1-111-11-113−33−300003−3−33−333−3000000−2i2i000000000000i3−i3i3−i3i−ii−i00000000
χ412-22-2-22-2222-2-2-2-222000000-1211-1-122-221-2-11-2-2-1-111-11-11−33−330000−333−33−3−330000002i−2i000000000000i3−i3i3−i3−ii−ii00000000
χ422-22-2-22-2222-2-2-2-222000000-1211-1-122-221-2-11-2-2-1-111-11-11−33−330000−333−33−3−33000000−2i2i000000000000−i3i3−i3i3i−ii−i00000000
χ432-2-222-2-222-222-2-2-220000002222-22-2-2-22-2-2-2-2222-222-2-22-200000000000000002i−2i00000000002i2i−2i−2i00000000000000000000
χ442-2-222-2-222-222-2-2-220000002222-22-2-2-22-2-2-2-2222-222-2-22-20000000000000000−2i2i0000000000−2i−2i2i2i00000000000000000000
χ452-2-22-222-22-22-22-22-22i−2i2i2i−2i−2i222-22-2-222-2-2-2-222-22-22-222-2-22i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ462-2-22-222-22-22-22-22-22i−2i2i2i−2i−2i2-12-22-21-1-11-21-22-11-11-11-1-1112i−2i−2i2i−iii−i−iii−i−iii−i0000000000000000000000000000−i3i3i3−i3−333−3
χ472-2-22-222-22-22-22-22-22i−2i2i2i−2i−2i2-12-22-21-1-11-21-22-11-11-11-1-1112i−2i−2i2i−iii−i−iii−i−iii−i0000000000000000000000000000i3−i3−i3i33−3−33
χ482-2-22-222-22-22-22-22-22i−2i2i2i−2i−2i-12-11-11-222-21-21-12-2-11-11-1-111−iii−i2i−2i−2i2i−iii−i−iii−i000000000000000000003−3−33i3−i3−i3i300000000
χ492-2-22-222-22-22-22-22-22i−2i2i2i−2i−2i-12-11-11-222-21-21-12-2-11-11-1-111−iii−i2i−2i−2i2i−iii−i−iii−i00000000000000000000−333−3−i3i3i3−i300000000
χ502-2-22-222-22-22-22-22-2−2i2i−2i−2i2i2i222-22-2-222-2-2-2-222-22-22-222-2-2−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ512-2-22-222-22-22-22-22-2−2i2i−2i−2i2i2i2-12-22-21-1-11-21-22-11-11-11-1-111−2i2i2i−2ii−i−iii−i−iii−i−ii0000000000000000000000000000−i3i3i3−i33−3−33
χ522-2-22-222-22-22-22-22-2−2i2i−2i−2i2i2i2-12-22-21-1-11-21-22-11-11-11-1-111−2i2i2i−2ii−i−iii−i−iii−i−ii0000000000000000000000000000i3−i3−i3i3−333−3
χ532-2-22-222-22-22-22-22-2−2i2i−2i−2i2i2i-12-11-11-222-21-21-12-2-11-11-1-111i−i−ii−2i2i2i−2ii−i−iii−i−ii000000000000000000003−3−33−i3i3i3−i300000000
χ542-2-22-222-22-22-22-22-2−2i2i−2i−2i2i2i-12-11-11-222-21-21-12-2-11-11-1-111i−i−ii−2i2i2i−2ii−i−iii−i−ii00000000000000000000−333−3i3−i3−i3i300000000
χ554444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-211111111-2-2-2-2-2-2-2-211111111000000000000000000000000000000000000
χ564444444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21111111122222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ574444-4-4-4-4444-4-44-4-40000004-24-4-4-4-22224-24-4-22-2-2-22222-20000000000000000000000000000000000000000000000000000
χ584444-4-4-4-4444-4-44-4-4000000-24-22224-4-4-4-24-224-4-2-2-22222-20000000000000000000000000000000000000000000000000000
χ594444-4-4-4-4444-4-44-4-4000000-2-2-2222-2222-2-2-22-22111-1-1-1-110000000033-3-3-3-333000000000000000000000000000000000000
χ604444-4-4-4-4444-4-44-4-4000000-2-2-2222-2222-2-2-22-22111-1-1-1-1100000000-3-33333-3-3000000000000000000000000000000000000
χ6144-4-444-4-44-4-44-444-40000004-2-444-42-2224-2-4-42-2-222-2-222-20000000000000000000000000000000000000000000000000000
χ6244-4-444-4-44-4-44-444-4000000-2-22-2-222-222-2-2222-21-1-111-1-11−2i3−2i32i32i30000i3i3i3i3−i3−i3−i3−i3000000000000000000000000000000000000
χ6344-4-444-4-44-4-44-444-4000000-2-22-2-222-222-2-2222-21-1-111-1-112i32i3−2i3−2i30000−i3−i3−i3−i3i3i3i3i3000000000000000000000000000000000000
χ6444-4-4-4-4444-4-4-444-44000000-24222-2-4-444-242-2-4-4-22222-2-2-20000000000000000000000000000000000000000000000000000
χ6544-4-4-4-4444-4-4-444-44000000-2-2222-222-2-2-2-22-2221-1-1-1-11110000−2i3−2i32i32i3i3i3−i3−i3i3i3−i3−i3000000000000000000000000000000000000
χ6644-4-4-4-4444-4-4-444-44000000-2-2222-222-2-2-2-22-2221-1-1-1-111100002i32i3−2i3−2i3−i3−i3i3i3−i3−i3i3i3000000000000000000000000000000000000
χ674-44-44-44-444-444-4-4-4000000-242-2224-44-42-4-2-2-44-2-22-22-2220000000000000000000000000000000000000000000000000000
χ684-44-44-44-444-444-4-4-4000000-2-22-222-22-2222-2-22-211-11-11-1-1000023−2323−23−33−33−33−33000000000000000000000000000000000000
χ694-44-44-44-444-444-4-4-4000000-2-22-222-22-2222-2-22-211-11-11-1-10000−2323−23233−33−33−33−3000000000000000000000000000000000000
χ704-44-4-44-4444-4-4-4-4440000004-2-4-444-2-22-2-424-422-2-222-22-220000000000000000000000000000000000000000000000000000
χ714-44-4-44-4444-4-4-4-444000000-2-222-2-2-2-22-222-222211-1-11-11-123−2323−230000−333−33−3−33000000000000000000000000000000000000
χ724-44-4-44-4444-4-4-4-444000000-2-222-2-2-2-22-222-222211-1-11-11-1−2323−232300003−3−33−333−3000000000000000000000000000000000000
χ734-4-444-4-444-444-4-4-440000004-244-44222-2-42-4-4-2-2-22-2-222-220000000000000000000000000000000000000000000000000000
χ744-4-444-4-444-444-4-4-44000000-24-2-22-2-4-4-442-42244-22-2-222-220000000000000000000000000000000000000000000000000000
χ754-4-444-4-444-444-4-4-44000000-2-2-2-22-2222-22222-2-21-111-1-11-1000000003i−3i3i−3i−3i3i−3i3i000000000000000000000000000000000000
χ764-4-444-4-444-444-4-4-44000000-2-2-2-22-2222-22222-2-21-111-1-11-100000000−3i3i−3i3i3i−3i3i−3i000000000000000000000000000000000000
χ774-4-44-444-44-44-44-44-44i−4i4i4i−4i−4i-2-2-22-222-2-22222-2-221-11-111-1-1−2i2i2i−2i−2i2i2i−2ii−i−iii−i−ii000000000000000000000000000000000000
χ784-4-44-444-44-44-44-44-4−4i4i−4i−4i4i4i-2-2-22-222-2-22222-2-221-11-111-1-12i−2i−2i2i2i−2i−2i2i−iii−i−iii−i000000000000000000000000000000000000
χ7966666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000222200000000-1-1-1-1-1-1-1-10000000000000000
χ8066666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000-2-2-2-200000000111111110000000000000000
χ8166666666-3-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000000022-2-200000000-1-1-1-111110000000000000000
χ8266666666-3-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000000000-2-222000000001111-1-1-1-10000000000000000
χ836666-6-6-6-6-3-3-333-33300−3i33i3−3i33i30000000000000000000000000000000000000000002i−2i000000003−33−3−i−iii0000000000000000
χ846666-6-6-6-6-3-3-333-33300−3i33i3−3i33i3000000000000000000000000000000000000000000−2i2i00000000−33−33ii−i−i0000000000000000
χ856666-6-6-6-6-3-3-333-333003i3−3i33i3−3i30000000000000000000000000000000000000000002i−2i00000000−33−33−i−iii0000000000000000
χ866666-6-6-6-6-3-3-333-333003i3−3i33i3−3i3000000000000000000000000000000000000000000−2i2i000000003−33−3ii−i−i0000000000000000
χ876-6-666-6-66-33-3-3333-30033−33−333300000000000000000000000000000000000000002i−2i0000000000−i−iii−i3i3−i3i30000000000000000
χ886-6-666-6-66-33-3-3333-30033−33−33330000000000000000000000000000000000000000−2i2i0000000000ii−i−ii3−i3i3−i30000000000000000
χ896-6-666-6-66-33-3-3333-300−333333−3300000000000000000000000000000000000000002i−2i0000000000−i−iiii3−i3i3−i30000000000000000
χ906-6-666-6-66-33-3-3333-300−333333−330000000000000000000000000000000000000000−2i2i0000000000ii−i−i−i3i3−i3i30000000000000000
χ916-6-66-666-6-33-33-33-336i−6i−3i−3i3i3i0000000000000000000000000000000000000000000000000000−i3i3i3−i3−333−30000000000000000
χ926-6-66-666-6-33-33-33-336i−6i−3i−3i3i3i0000000000000000000000000000000000000000000000000000i3−i3−i3i33−3−330000000000000000
χ936-6-66-666-6-33-33-33-33−6i6i3i3i−3i−3i0000000000000000000000000000000000000000000000000000−i3i3i3−i33−3−330000000000000000
χ946-6-66-666-6-33-33-33-33−6i6i3i3i−3i−3i0000000000000000000000000000000000000000000000000000i3−i3−i3i3−333−30000000000000000
χ951212-12-121212-12-12-666-66-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ961212-12-12-12-121212-6666-6-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-1212-1212-1212-12-6-66-6-66660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-1212-12-1212-1212-6-66666-6-60000000000000000000000000000000000000000000000000000000000000000000000000000000000

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