Finite Group Databasebeta

← Group #13140210

Character table — Group #13140210

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order122222223666666644121212123366666666666666366666661212121212121212121212121212121222444444444466661212121212121212121212121212121212121212
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
χ922222222222222222222222-122222-1-1-1-1-12-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100002222000000000000-1-1-1-1-1-1-1-100000000
χ1022222222222222222222222-122222-1-1-1-1-12-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000-2-2-2-20000000000001111111100000000
χ112222222222222222222222-12-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000022220000000000000000-1-1-1-1-1-1-1-1
χ122222222222222222222222-12-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-2000000000000000011111111
χ132222222222222222-2-2-2-2-2-22-122222-1-1-1-1-12-1-12-1-1-1-1-1-1-1-11111-2-2-2-211111111000022-2-2000000000000-1-1-1-1111100000000
χ142222222222222222-2-2-2-2-2-22-122222-1-1-1-1-12-1-12-1-1-1-1-1-1-1-11111-2-2-2-2111111110000-2-2220000000000001111-1-1-1-100000000
χ152222222222222222-2-2-2-2-2-2-12-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000000022-2-20000000000000000-1-1-1-11111
χ162222222222222222-2-2-2-2-2-2-12-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-1-2-2-2-211111111111100000000-2-22200000000000000001111-1-1-1-1
χ17222-2-2-2-22222-2-2-22-20000002222-2-2-222-2-22-2-2-22222-2-2-2-22000000000000000000002i−2i000000000000002i2i−2i−2i000000000000
χ18222-2-2-2-22222-2-2-22-20000002222-2-2-222-2-22-2-2-22222-2-2-2-2200000000000000000000−2i2i00000000000000−2i−2i2i2i000000000000
χ19222-2-2-2-22222-2-2-22-20000002-122-2-2-2-1-111-1-2112-1-1-11111-1−i3−i3i3i30000−i3−i3−i3−i3i3i3i3i300002i−2i00000000000000−i−iii33−3−300000000
χ20222-2-2-2-22222-2-2-22-20000002-122-2-2-2-1-111-1-2112-1-1-11111-1−i3−i3i3i30000−i3−i3−i3−i3i3i3i3i30000−2i2i00000000000000ii−i−i−3−33300000000
χ21222-2-2-2-22222-2-2-22-20000002-122-2-2-2-1-111-1-2112-1-1-11111-1i3i3−i3−i30000i3i3i3i3−i3−i3−i3−i300002i−2i00000000000000−i−iii−3−33300000000
χ22222-2-2-2-22222-2-2-22-20000002-122-2-2-2-1-111-1-2112-1-1-11111-1i3i3−i3−i30000i3i3i3i3−i3−i3−i3−i30000−2i2i00000000000000ii−i−i33−3−300000000
χ2322-222-2-2-222-222-2-2-2000000222-222-22-2-2-2-2-222-222-222-2-2-20000000000000000002i−2i0000000000002i2i−2i−2i0000000000000000
χ2422-222-2-2-222-222-2-2-2000000222-222-22-2-2-2-2-222-222-222-2-2-2000000000000000000−2i2i000000000000−2i−2i2i2i0000000000000000
χ2522-2-2-222-222-2-2-22-22000000222-2-2-222-222-22-2-2-222-2-2-222-2000000000000000000000000002i−2i000000000000000000002i2i−2i−2i
χ2622-2-2-222-222-2-2-22-22000000222-2-2-222-222-22-2-2-222-2-2-222-200000000000000000000000000−2i2i00000000000000000000−2i−2i2i2i
χ2722-2-2-222-222-2-2-22-22000000-12-1111-12-222-2-1-2-21-1-1111-1-11000033−3−333−3−333−3−300000000002i−2i0000000000000000−i3−i3i3i3−i−iii
χ2822-2-2-222-222-2-2-22-22000000-12-1111-12-222-2-1-2-21-1-1111-1-11000033−3−333−3−333−3−30000000000−2i2i0000000000000000i3i3−i3−i3ii−i−i
χ2922-2-2-222-222-2-2-22-22000000-12-1111-12-222-2-1-2-21-1-1111-1-110000−3−333−3−333−3−33300000000002i−2i0000000000000000i3i3−i3−i3−i−iii
χ3022-2-2-222-222-2-2-22-22000000-12-1111-12-222-2-1-2-21-1-1111-1-110000−3−333−3−333−3−3330000000000−2i2i0000000000000000−i3−i3i3i3ii−i−i
χ312-222-22-2-22-222-22-2-22i−2i2i2i−2i−2i22-222-2-2-222-2-222-2-22-222-22-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000
χ322-222-22-2-22-222-22-2-22i−2i2i2i−2i−2i2-1-222-2-21-1-1112-11-2-11-1-11-111−ii−ii2i−2i2i−2i−ii−ii−ii−ii000000000000000000003−33−3−i3i3−i3i300000000
χ332-222-22-2-22-222-22-2-22i−2i2i2i−2i−2i2-1-222-2-21-1-1112-11-2-11-1-11-111−ii−ii2i−2i2i−2i−ii−ii−ii−ii00000000000000000000−33−33i3−i3i3−i300000000
χ342-222-22-2-22-222-22-2-22i−2i2i2i−2i−2i-121-1-111-222-2-2-12-21-11-1-11-1112i−2i2i−2i−ii−ii−ii−ii−ii−ii0000000000000000000000000000−i3i3−i3i33−33−3
χ352-222-22-2-22-222-22-2-22i−2i2i2i−2i−2i-121-1-111-222-2-2-12-21-11-1-11-1112i−2i2i−2i−ii−ii−ii−ii−ii−ii0000000000000000000000000000i3−i3i3−i3−33−33
χ362-222-22-2-22-222-22-2-2−2i2i−2i−2i2i2i22-222-2-2-222-2-222-2-22-222-22-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000
χ372-222-22-2-22-222-22-2-2−2i2i−2i−2i2i2i2-1-222-2-21-1-1112-11-2-11-1-11-111i−ii−i−2i2i−2i2ii−ii−ii−ii−i000000000000000000003−33−3i3−i3i3−i300000000
χ382-222-22-2-22-222-22-2-2−2i2i−2i−2i2i2i2-1-222-2-21-1-1112-11-2-11-1-11-111i−ii−i−2i2i−2i2ii−ii−ii−ii−i00000000000000000000−33−33−i3i3−i3i300000000
χ392-222-22-2-22-222-22-2-2−2i2i−2i−2i2i2i-121-1-111-222-2-2-12-21-11-1-11-111−2i2i−2i2ii−ii−ii−ii−ii−ii−i0000000000000000000000000000−i3i3−i3i3−33−33
χ402-222-22-2-22-222-22-2-2−2i2i−2i−2i2i2i-121-1-111-222-2-2-12-21-11-1-11-111−2i2i−2i2ii−ii−ii−ii−ii−ii−i0000000000000000000000000000i3−i3i3−i33−33−3
χ412-22-22-22-22-22-22-2-2200000022-22-222-22-22-2-2-22-22-22-22-22-200000000000000000000002i−2i00000000000000002i−2i−2i2i00000000
χ422-22-22-22-22-22-22-2-2200000022-22-222-22-22-2-2-22-22-22-22-22-20000000000000000000000−2i2i0000000000000000−2i2i2i−2i00000000
χ432-22-22-22-22-22-22-2-220000002-1-22-2221-11-11-21-1-2-11-11-11-113−3−3300003−33−3−33−330000002i−2i000000000000i3−i3−i3i3−iii−i00000000
χ442-22-22-22-22-22-22-2-220000002-1-22-2221-11-11-21-1-2-11-11-11-113−3−3300003−33−3−33−33000000−2i2i000000000000−i3i3i3−i3i−i−ii00000000
χ452-22-22-22-22-22-22-2-220000002-1-22-2221-11-11-21-1-2-11-11-11-11−333−30000−33−333−33−30000002i−2i000000000000−i3i3i3−i3−iii−i00000000
χ462-22-22-22-22-22-22-2-220000002-1-22-2221-11-11-21-1-2-11-11-11-11−333−30000−33−333−33−3000000−2i2i000000000000i3−i3−i3i3i−i−ii00000000
χ472-2-22-2-2222-2-22-2-22200000022-2-22-22-2-2-222-22-222-2-22-2-22200000000000000002-2000000000022-2-200000000000000000000
χ482-2-22-2-2222-2-22-2-22200000022-2-22-22-2-2-222-22-222-2-22-2-2220000000000000000-220000000000-2-22200000000000000000000
χ492-2-2-222-222-2-2-2222-200000022-2-2-22-2-2-22-222-2222-2-2-222-220000000000000000000000002-20000000000000000002-2-220000
χ502-2-2-222-222-2-2-2222-200000022-2-2-22-2-2-22-222-2222-2-2-222-22000000000000000000000000-22000000000000000000-222-20000
χ512-2-2-222-222-2-2-2222-2000000-12111-11-2-22-22-1-22-1-1111-1-11-10000−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3000000002-2000000000000000000-111-1−i3i3i3−i3
χ522-2-2-222-222-2-2-2222-2000000-12111-11-2-22-22-1-22-1-1111-1-11-10000−i3i3i3−i3−i3i3i3−i3−i3i3i3−i300000000-220000000000000000001-1-11i3−i3−i3i3
χ532-2-2-222-222-2-2-2222-2000000-12111-11-2-22-22-1-22-1-1111-1-11-10000i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3000000002-2000000000000000000-111-1i3−i3−i3i3
χ542-2-2-222-222-2-2-2222-2000000-12111-11-2-22-22-1-22-1-1111-1-11-10000i3−i3−i3i3i3−i3−i3i3i3−i3−i3i300000000-220000000000000000001-1-11−i3i3i3−i3
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
χ57444-4-4-4-44444-4-4-44-4000000-24-2-222244-4-442-4-4-2-2-2-22222-20000000000000000000000000000000000000000000000000000
χ58444-4-4-4-44444-4-4-44-4000000-2-2-2-2222-2-222-2222-2111-1-1-1-11−2i3−2i32i32i30000i3i3i3i3−i3−i3−i3−i3000000000000000000000000000000000000
χ59444-4-4-4-44444-4-4-44-4000000-2-2-2-2222-2-222-2222-2111-1-1-1-112i32i3−2i3−2i30000−i3−i3−i3−i3i3i3i3i3000000000000000000000000000000000000
χ6044-444-4-4-444-444-4-4-40000004-24-444-4-22222-4-2-2-4-2-22-2-22220000000000000000000000000000000000000000000000000000
χ6144-444-4-4-444-444-4-4-4000000-24-22-2-224-4-4-4-42442-2-22-2-22220000000000000000000000000000000000000000000000000000
χ6244-444-4-4-444-444-4-4-4000000-2-2-22-2-22-222222-2-2211-111-1-1-1000000003i3i−3i−3i−3i−3i3i3i000000000000000000000000000000000000
χ6344-444-4-4-444-444-4-4-4000000-2-2-22-2-22-222222-2-2211-111-1-1-100000000−3i−3i3i3i3i3i−3i−3i000000000000000000000000000000000000
χ6444-4-4-444-444-4-4-44-440000004-24-4-4-44-22-2-22422-4-2-2222-2-220000000000000000000000000000000000000000000000000000
χ6544-4-4-444-444-4-4-44-44000000-2-2-2222-2-22-2-22-222211-1-1-111-100002323−23−23−3−333−3−333000000000000000000000000000000000000
χ6644-4-4-444-444-4-4-44-44000000-2-2-2222-2-22-2-22-222211-1-1-111-10000−23−23232333−3−333−3−3000000000000000000000000000000000000
χ674-444-44-4-44-444-44-4-44i−4i4i4i−4i−4i-2-22-2-2222-2-222-2-2221-111-11-1-1−2i2i−2i2i−2i2i−2i2ii−ii−ii−ii−i000000000000000000000000000000000000
χ684-444-44-4-44-444-44-4-4−4i4i−4i−4i4i4i-2-22-2-2222-2-222-2-2221-111-11-1-12i−2i2i−2i2i−2i2i−2i−ii−ii−ii−ii000000000000000000000000000000000000
χ694-44-44-44-44-44-44-4-44000000-242-22-2-2-44-44-42-442-22-22-22-220000000000000000000000000000000000000000000000000000
χ704-44-44-44-44-44-44-4-44000000-2-22-22-2-22-22-2222-221-11-11-11-123−23−23230000−33−333−33−3000000000000000000000000000000000000
χ714-44-44-44-44-44-44-4-44000000-2-22-22-2-22-22-2222-221-11-11-11-1−232323−2300003−33−3−33−33000000000000000000000000000000000000
χ724-4-44-4-4444-4-44-4-4440000004-2-4-44-44222-2-2-4-224-222-222-2-20000000000000000000000000000000000000000000000000000
χ734-4-44-4-4444-4-44-4-444000000-2422-22-2-4-4-44424-4-2-222-222-2-20000000000000000000000000000000000000000000000000000
χ744-4-44-4-4444-4-44-4-444000000-2-222-22-2222-2-22-22-21-1-11-1-111000000003-3-33-333-3000000000000000000000000000000000000
χ754-4-44-4-4444-4-44-4-444000000-2-222-22-2222-2-22-22-21-1-11-1-11100000000-333-33-3-33000000000000000000000000000000000000
χ764-4-4-444-444-4-4-4444-40000004-2-4-4-44-422-22-242-24-2222-2-22-20000000000000000000000000000000000000000000000000000
χ774-4-4-444-444-4-4-4444-4000000-2-2222-2222-22-2-22-2-21-1-1-111-110000−2i32i32i3−2i3i3−i3−i3i3i3−i3−i3i3000000000000000000000000000000000000
χ784-4-4-444-444-4-4-4444-4000000-2-2222-2222-22-2-22-2-21-1-1-111-1100002i3−2i3−2i32i3−i3i3i3−i3−i3i3i3−i3000000000000000000000000000000000000
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
χ8366-666-6-6-6-3-33-3-33330033−3333−330000000000000000000000000000000000000000002i−2i00000000−i3i3−i3i3−i−iii0000000000000000
χ8466-666-6-6-6-3-33-3-33330033−3333−33000000000000000000000000000000000000000000−2i2i00000000i3−i3i3−i3ii−i−i0000000000000000
χ8566-666-6-6-6-3-33-3-333300−3333−33330000000000000000000000000000000000000000002i−2i00000000i3−i3i3−i3−i−iii0000000000000000
χ8666-666-6-6-6-3-33-3-333300−3333−3333000000000000000000000000000000000000000000−2i2i00000000−i3i3−i3i3ii−i−i0000000000000000
χ876-666-66-6-6-33-3-33-3336i−6i−3i−3i3i3i0000000000000000000000000000000000000000000000000000−i3i3i3−i33−33−30000000000000000
χ886-666-66-6-6-33-3-33-3336i−6i−3i−3i3i3i0000000000000000000000000000000000000000000000000000i3−i3−i3i3−33−330000000000000000
χ896-666-66-6-6-33-3-33-333−6i6i3i3i−3i−3i0000000000000000000000000000000000000000000000000000−i3i3i3−i3−33−330000000000000000
χ906-666-66-6-6-33-3-33-333−6i6i3i3i−3i−3i0000000000000000000000000000000000000000000000000000i3−i3−i3i33−33−30000000000000000
χ916-6-66-6-666-333-333-3-300−3i33i33i3−3i300000000000000000000000000000000000000002-20000000000-1-111−i3i3i3−i30000000000000000
χ926-6-66-6-666-333-333-3-300−3i33i33i3−3i30000000000000000000000000000000000000000-22000000000011-1-1i3−i3−i3i30000000000000000
χ936-6-66-6-666-333-333-3-3003i3−3i3−3i33i300000000000000000000000000000000000000002-20000000000-1-111i3−i3−i3i30000000000000000
χ946-6-66-6-666-333-333-3-3003i3−3i3−3i33i30000000000000000000000000000000000000000-22000000000011-1-1−i3i3i3−i30000000000000000
χ95121212-12-12-12-1212-6-6-6666-660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ961212-12-12-121212-12-6-6666-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-1212-1212-1212-12-66-66-666-60000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12-12-121212-1212-6666-6-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000

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