Finite Group Databasebeta

← Group #13140110

Character table — Group #13140110

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order1222222236666666441212121233666666666666663666666612121212121212121212121212121212444444444444121212121212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ311111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ922222222222222222222222-122222-1-1-1-1-12-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000022000022000000000000-1-1-1-1-1-1-1-10000
χ1022222222222222222222222-122222-1-1-1-1-12-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-20000-2-2000000000000111111110000
χ112222222222222222222222-12-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122000022000000000000-1-1-1-100000000-1-1-1-1
χ122222222222222222222222-12-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-20000-2-20000000000001111000000001111
χ132222222222222222-2-2-2-2-2-22-122222-1-1-1-1-12-1-12-1-1-1-1-1-1-1-11111-2-2-2-2111111110000220000-2-20000000000001111-1-1-1-10000
χ142222222222222222-2-2-2-2-2-22-122222-1-1-1-1-12-1-12-1-1-1-1-1-1-1-11111-2-2-2-2111111110000-2-2000022000000000000-1-1-1-111110000
χ152222222222222222-2-2-2-2-2-2-12-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111220000-2-2000000000000-1-1-1-1000000001111
χ162222222222222222-2-2-2-2-2-2-12-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111-2-2000022000000000000111100000000-1-1-1-1
χ172222-2-2-2-22222-2-2-2-20000002222-2-2-2222-2-22-2-2-22222-2-2-2-200000000000000002-200000000000000000022-2-2000000000000
χ182222-2-2-2-22222-2-2-2-20000002222-2-2-2222-2-22-2-2-22222-2-2-2-20000000000000000-22000000000000000000-2-222000000000000
χ192222-2-2-2-22222-2-2-2-2000000-12-1-1111222-2-2-1-2-21-1-1-1-11111000033−3−33333−3−3−3−32-2000000000000000000-1-1110000000033−3−3
χ202222-2-2-2-22222-2-2-2-2000000-12-1-1111222-2-2-1-2-21-1-1-1-11111000033−3−33333−3−3−3−3-2200000000000000000011-1-100000000−3−333
χ212222-2-2-2-22222-2-2-2-2000000-12-1-1111222-2-2-1-2-21-1-1-1-111110000−3−333−3−3−3−333332-2000000000000000000-1-11100000000−3−333
χ222222-2-2-2-22222-2-2-2-2000000-12-1-1111222-2-2-1-2-21-1-1-1-111110000−3−333−3−3−3−33333-2200000000000000000011-1-10000000033−3−3
χ2322-2-22-22-222-2-222-2-2000000222-22-2-22-2-2-22-22-2222-2-22-2-220000000000000000000000002i−2i0000002i2i−2i−2i0000000000000000
χ2422-2-22-22-222-2-222-2-2000000222-22-2-22-2-2-22-22-2222-2-22-2-22000000000000000000000000−2i2i000000−2i−2i2i2i0000000000000000
χ2522-2-2-22-2222-2-2-2-222000000222-2-2222-2-22-2-2-22-222-2-2-222-2000000000000000000002i−2i00000000000000000000002i2i−2i−2i0000
χ2622-2-2-22-2222-2-2-2-222000000222-2-2222-2-22-2-2-22-222-2-2-222-200000000000000000000−2i2i0000000000000000000000−2i−2i2i2i0000
χ2722-2-2-22-2222-2-2-2-2220000002-12-2-222-111-11-21-1-2-1-1111-1-1133−3−3000033−3−333−3−300002i−2i000000000000000000−i3−i3i3i3−i−iii0000
χ2822-2-2-22-2222-2-2-2-2220000002-12-2-222-111-11-21-1-2-1-1111-1-1133−3−3000033−3−333−3−30000−2i2i000000000000000000i3i3−i3−i3ii−i−i0000
χ2922-2-2-22-2222-2-2-2-2220000002-12-2-222-111-11-21-1-2-1-1111-1-11−3−3330000−3−333−3−33300002i−2i000000000000000000i3i3−i3−i3−i−iii0000
χ3022-2-2-22-2222-2-2-2-2220000002-12-2-222-111-11-21-1-2-1-1111-1-11−3−3330000−3−333−3−3330000−2i2i000000000000000000−i3−i3i3i3ii−i−i0000
χ312-22-22-2-222-22-22-22-200000022-2222-2-22-2-2-2-222-22-22-222-2-20000000000000000002i−2i000000002i2i−2i−2i00000000000000000000
χ322-22-22-2-222-22-22-22-200000022-2222-2-22-2-2-2-222-22-22-222-2-2000000000000000000−2i2i00000000−2i−2i2i2i00000000000000000000
χ332-22-2-222-22-22-2-22-2200000022-22-2-22-22-222-2-2-222-22-2-2-222000000000000000000000000002i−2i0000000000002i−2i2i−2i00000000
χ342-22-2-222-22-22-2-22-2200000022-22-2-22-22-222-2-2-222-22-2-2-22200000000000000000000000000−2i2i000000000000−2i2i−2i2i00000000
χ352-22-2-222-22-22-2-22-220000002-1-22-2-221-11-1-1-2112-11-1111-1-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i300000000002i−2i000000000000−ii−ii3−33−30000
χ362-22-2-222-22-22-2-22-220000002-1-22-2-221-11-1-1-2112-11-1111-1-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i30000000000−2i2i000000000000i−ii−i−33−330000
χ372-22-2-222-22-22-2-22-220000002-1-22-2-221-11-1-1-2112-11-1111-1-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i300000000002i−2i000000000000−ii−ii−33−330000
χ382-22-2-222-22-22-2-22-220000002-1-22-2-221-11-1-1-2112-11-1111-1-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i30000000000−2i2i000000000000i−ii−i3−33−30000
χ392-2-2222-2-22-2-222-2-222i−2i2i2i−2i−2i22-2-22-22-2-222-222-2-22-2-222-22-22i−2i−2i2i2i−2i2i−2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000000000
χ402-2-2222-2-22-2-222-2-222i−2i2i2i−2i−2i2-1-2-22-2211-1-112-11-2-111-1-11-11−iii−i2i−2i2i−2i−iii−i−iii−i0000000000000000000000003−3−33i3−i3−i3i30000
χ412-2-2222-2-22-2-222-2-222i−2i2i2i−2i−2i2-1-2-22-2211-1-112-11-2-111-1-11-11−iii−i2i−2i2i−2i−iii−i−iii−i000000000000000000000000−333−3−i3i3i3−i30000
χ422-2-2222-2-22-2-222-2-222i−2i2i2i−2i−2i-1211-11-1-2-222-2-12-21-111-1-11-112i−2i−2i2i−ii−ii−iii−i−iii−i00000000000000000000−i3i3−i3i3000000003−33−3
χ432-2-2222-2-22-2-222-2-222i−2i2i2i−2i−2i-1211-11-1-2-222-2-12-21-111-1-11-112i−2i−2i2i−ii−ii−iii−i−iii−i00000000000000000000i3−i3i3−i300000000−33−33
χ442-2-2222-2-22-2-222-2-22−2i2i−2i−2i2i2i22-2-22-22-2-222-222-2-22-2-222-22-2−2i2i2i−2i−2i2i−2i2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000000000
χ452-2-2222-2-22-2-222-2-22−2i2i−2i−2i2i2i2-1-2-22-2211-1-112-11-2-111-1-11-11i−i−ii−2i2i−2i2ii−i−iii−i−ii0000000000000000000000003−3−33−i3i3i3−i30000
χ462-2-2222-2-22-2-222-2-22−2i2i−2i−2i2i2i2-1-2-22-2211-1-112-11-2-111-1-11-11i−i−ii−2i2i−2i2ii−i−iii−i−ii000000000000000000000000−333−3i3−i3−i3i30000
χ472-2-2222-2-22-2-222-2-22−2i2i−2i−2i2i2i-1211-11-1-2-222-2-12-21-111-1-11-11−2i2i2i−2ii−ii−ii−i−iii−i−ii00000000000000000000−i3i3−i3i300000000−33−33
χ482-2-2222-2-22-2-222-2-22−2i2i−2i−2i2i2i-1211-11-1-2-222-2-12-21-111-1-11-11−2i2i2i−2ii−ii−ii−i−iii−i−ii00000000000000000000i3−i3i3−i3000000003−33−3
χ492-2-22-2-2222-2-22-222-200000022-2-2-22-2-2-22-222-2222-2-22-22-2200000000000000000000002-20000000000000000000000002-2-22
χ502-2-22-2-2222-2-22-222-200000022-2-2-22-2-2-22-222-2222-2-22-22-220000000000000000000000-22000000000000000000000000-222-2
χ512-2-22-2-2222-2-22-222-2000000-12111-11-2-22-22-1-22-1-111-11-11-10000−i3i3i3−i3−i3i3i3−i3i3−i3−i3i30000002-2000000000000−i3i3i3−i300000000-111-1
χ522-2-22-2-2222-2-22-222-2000000-12111-11-2-22-22-1-22-1-111-11-11-10000−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3000000-22000000000000i3−i3−i3i3000000001-1-11
χ532-2-22-2-2222-2-22-222-2000000-12111-11-2-22-22-1-22-1-111-11-11-10000i3−i3−i3i3i3−i3−i3i3−i3i3i3−i30000002-2000000000000i3−i3−i3i300000000-111-1
χ542-2-22-2-2222-2-22-222-2000000-12111-11-2-22-22-1-22-1-111-11-11-10000i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3000000-22000000000000−i3i3i3−i3000000001-1-11
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
χ574444-4-4-4-44444-4-4-4-40000004-244-4-4-4-2-2-222422-4-2-2-2-222220000000000000000000000000000000000000000000000000000
χ584444-4-4-4-44444-4-4-4-4000000-2-2-2-2222-2-2-222-22221111-1-1-1-100002323−23−23−3−3−3−33333000000000000000000000000000000000000
χ594444-4-4-4-44444-4-4-4-4000000-2-2-2-2222-2-2-222-22221111-1-1-1-10000−23−2323233333−3−3−3−3000000000000000000000000000000000000
χ6044-4-44-44-444-4-444-4-40000004-24-44-4-4-2222-2-4-224-2-222-222-20000000000000000000000000000000000000000000000000000
χ6144-4-44-44-444-4-444-4-4000000-24-22-2224-4-4-4424-4-2-2-222-222-20000000000000000000000000000000000000000000000000000
χ6244-4-44-44-444-4-444-4-4000000-2-2-22-222-2222-22-22-211-1-11-1-110000000033-3-3-3-333000000000000000000000000000000000000
χ6344-4-44-44-444-4-444-4-4000000-2-2-22-222-2222-22-22-211-1-11-1-1100000000-3-33333-3-3000000000000000000000000000000000000
χ6444-4-4-44-4444-4-4-4-444000000-24-222-2-24-4-44-42-442-2-2222-2-220000000000000000000000000000000000000000000000000000
χ6544-4-4-44-4444-4-4-4-444000000-2-2-222-2-2-222-2222-2211-1-1-111-12323−23−230000−3−333−3−333000000000000000000000000000000000000
χ6644-4-4-44-4444-4-4-4-444000000-2-2-222-2-2-222-2222-2211-1-1-111-1−23−232323000033−3−333−3−3000000000000000000000000000000000000
χ674-44-44-4-444-44-44-44-40000004-2-4444-42-2222-4-2-2-4-22-22-2-2220000000000000000000000000000000000000000000000000000
χ684-44-44-4-444-44-44-44-4000000-242-2-2-22-44-4-4-42442-22-22-2-2220000000000000000000000000000000000000000000000000000
χ694-44-44-4-444-44-44-44-4000000-2-22-2-2-222-22222-2-221-11-111-1-1000000003i−3i3i−3i−3i3i−3i3i000000000000000000000000000000000000
χ704-44-44-4-444-44-44-44-4000000-2-22-2-2-222-22222-2-221-11-111-1-100000000−3i3i−3i3i3i−3i3i−3i000000000000000000000000000000000000
χ714-44-4-444-44-44-4-44-44000000-242-222-2-44-4442-4-4-2-22-2222-2-20000000000000000000000000000000000000000000000000000
χ724-44-4-444-44-44-4-44-44000000-2-22-222-22-22-2-2222-21-11-1-1-111−2i32i3−2i32i30000i3−i3i3−i3i3−i3i3−i3000000000000000000000000000000000000
χ734-44-4-444-44-44-4-44-44000000-2-22-222-22-22-2-2222-21-11-1-1-1112i3−2i32i3−2i30000−i3i3−i3i3−i3i3−i3i3000000000000000000000000000000000000
χ744-4-4444-4-44-4-444-4-444i−4i4i4i−4i−4i-2-222-22-222-2-22-2-2221-1-111-11-1−2i2i2i−2i−2i2i−2i2ii−i−iii−i−ii000000000000000000000000000000000000
χ754-4-4444-4-44-4-444-4-44−4i4i−4i−4i4i4i-2-222-22-222-2-22-2-2221-1-111-11-12i−2i−2i2i2i−2i2i−2i−iii−i−iii−i000000000000000000000000000000000000
χ764-4-44-4-4444-4-44-444-40000004-2-4-4-44-422-22-242-24-222-22-22-20000000000000000000000000000000000000000000000000000
χ774-4-44-4-4444-4-44-444-4000000-2-2222-2222-22-2-22-2-21-1-11-11-110000−2i32i32i3−2i3i3−i3−i3i3−i3i3i3−i3000000000000000000000000000000000000
χ784-4-44-4-4444-4-44-444-4000000-2-2222-2222-22-2-22-2-21-1-11-11-1100002i3−2i3−2i32i3−i3i3i3−i3i3−i3−i3i3000000000000000000000000000000000000
χ7966666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000002200002200-1-1-1-1-1-1-1-10000000000000000
χ8066666666-3-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000000000-2-20000-2-200111111110000000000000000
χ8166666666-3-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000000000220000-2-200-1-1-1-111110000000000000000
χ8266666666-3-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000000000-2-2000022001111-1-1-1-10000000000000000
χ8366-6-66-66-6-3-333-3-33300−3i33i3−3i33i30000000000000000000000000000000000000000000000002i−2i003−33−3−i−iii0000000000000000
χ8466-6-66-66-6-3-333-3-33300−3i33i3−3i33i3000000000000000000000000000000000000000000000000−2i2i00−33−33ii−i−i0000000000000000
χ8566-6-66-66-6-3-333-3-333003i3−3i33i3−3i30000000000000000000000000000000000000000000000002i−2i00−33−33−i−iii0000000000000000
χ8666-6-66-66-6-3-333-3-333003i3−3i33i3−3i3000000000000000000000000000000000000000000000000−2i2i003−33−3ii−i−i0000000000000000
χ876-66-66-6-66-33-33-33-330033−33−33330000000000000000000000000000000000000000002i−2i00000000−i−iii−i3i3−i3i30000000000000000
χ886-66-66-6-66-33-33-33-330033−33−3333000000000000000000000000000000000000000000−2i2i00000000ii−i−ii3−i3i3−i30000000000000000
χ896-66-66-6-66-33-33-33-3300−333333−330000000000000000000000000000000000000000002i−2i00000000−i−iiii3−i3i3−i30000000000000000
χ906-66-66-6-66-33-33-33-3300−333333−33000000000000000000000000000000000000000000−2i2i00000000ii−i−i−i3i3−i3i30000000000000000
χ916-6-6666-6-6-333-3-333-36i−6i−3i−3i3i3i0000000000000000000000000000000000000000000000000000−i3i3i3−i3−333−30000000000000000
χ926-6-6666-6-6-333-3-333-36i−6i−3i−3i3i3i0000000000000000000000000000000000000000000000000000i3−i3−i3i33−3−330000000000000000
χ936-6-6666-6-6-333-3-333-3−6i6i3i3i−3i−3i0000000000000000000000000000000000000000000000000000−i3i3i3−i33−3−330000000000000000
χ946-6-6666-6-6-333-3-333-3−6i6i3i3i−3i−3i0000000000000000000000000000000000000000000000000000i3−i3−i3i3−333−30000000000000000
χ9512121212-12-12-12-12-6-6-6-666660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ961212-12-12-1212-1212-6-66666-6-60000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-1212-12-121212-12-66-666-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12-1212-12-121212-666-66-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000

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