Finite Group Databasebeta

← Group #13140139

Character table — Group #13140139

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order1222222236666666441212121233666666666666663666666612121212121212121212121212121212444444444444121212121212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
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
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ922222222222222222222222-122222-1-1-1-1-12-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122002200000000000000-1-1-1-1-1-1-1-100000000
χ1022222222222222222222222-122222-1-1-1-1-12-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-200-2-2000000000000001111111100000000
χ112222222222222222222222-12-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000002200220000000000000000-1-1-1-1-1-1-1-1
χ122222222222222222222222-12-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000-2-200-2-2000000000000000011111111
χ132222222222222222-2-2-2-2-2-22-122222-1-1-1-1-12-1-12-1-1-1-1-1-1-1-11111-2-2-2-2111111112200-2-200000000000000-1-1-1-1111100000000
χ142222222222222222-2-2-2-2-2-22-122222-1-1-1-1-12-1-12-1-1-1-1-1-1-1-11111-2-2-2-211111111-2-20022000000000000001111-1-1-1-100000000
χ152222222222222222-2-2-2-2-2-2-12-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000002200-2-20000000000000000-1-1-1-11111
χ162222222222222222-2-2-2-2-2-2-12-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111000000-2-2002200000000000000001111-1-1-1-1
χ17222-22-2-2-22222-2-2-2-200000022222-2-222-2-2-2-22-2-22222-2-2-2-200000000000000002-200000000000000000022-2-2000000000000
χ18222-22-2-2-22222-2-2-2-200000022222-2-222-2-2-2-22-2-22222-2-2-2-20000000000000000-22000000000000000000-2-222000000000000
χ19222-22-2-2-22222-2-2-2-20000002-1222-2-2-1-1111-2-11-2-1-1-1-1111133−3−300003333−3−3−3−32-2000000000000000000-1-11133−3−300000000
χ20222-22-2-2-22222-2-2-2-20000002-1222-2-2-1-1111-2-11-2-1-1-1-1111133−3−300003333−3−3−3−3-2200000000000000000011-1-1−3−33300000000
χ21222-22-2-2-22222-2-2-2-20000002-1222-2-2-1-1111-2-11-2-1-1-1-11111−3−3330000−3−3−3−333332-2000000000000000000-1-111−3−33300000000
χ22222-22-2-2-22222-2-2-2-20000002-1222-2-2-1-1111-2-11-2-1-1-1-11111−3−3330000−3−3−3−33333-2200000000000000000011-1-133−3−300000000
χ2322-22-22-2-222-2-22-22-2000000222-2-2222-222-2-2-2-2-222-2-222-2-20000000000000000002-20000000022-2-200000000000000000000
χ2422-22-22-2-222-2-22-22-2000000222-2-2222-222-2-2-2-2-222-2-222-2-2000000000000000000-2200000000-2-22200000000000000000000
χ2522-2-2-2-22222-2-2-22-22000000222-2-2-2-22-2-2-222-22222-2-2-2-22200000000000000000000002-20000000000000000000022-2-20000
χ2622-2-2-2-22222-2-2-22-22000000222-2-2-2-22-2-2-222-22222-2-2-2-2220000000000000000000000-2200000000000000000000-2-2220000
χ2722-2-2-2-22222-2-2-22-22000000-12-111112-2-2-22-1-22-1-1-11111-1-10000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000002-200000000000000000000-1-111−i3−i3i3i3
χ2822-2-2-2-22222-2-2-22-22000000-12-111112-2-2-22-1-22-1-1-11111-1-10000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000000-220000000000000000000011-1-1i3i3−i3−i3
χ2922-2-2-2-22222-2-2-22-22000000-12-111112-2-2-22-1-22-1-1-11111-1-10000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000002-200000000000000000000-1-111i3i3−i3−i3
χ3022-2-2-2-22222-2-2-22-22000000-12-111112-2-2-22-1-22-1-1-11111-1-10000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000000-220000000000000000000011-1-1−i3−i3i3i3
χ312-222-2-2-222-22-22-2-2200000022-22-22-2-222-22-2-2-222-22-22-2-22000000000000000000002i−2i0000000000000000002i−2i2i−2i00000000
χ322-222-2-2-222-22-22-2-2200000022-22-22-2-222-22-2-2-222-22-22-2-2200000000000000000000−2i2i000000000000000000−2i2i−2i2i00000000
χ332-222-2-2-222-22-22-2-220000002-1-22-22-21-1-11-1-2112-11-11-111-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i300002i−2i000000000000003−33−3−ii−ii00000000
χ342-222-2-2-222-22-22-2-220000002-1-22-22-21-1-11-1-2112-11-11-111-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i30000−2i2i00000000000000−33−33i−ii−i00000000
χ352-222-2-2-222-22-22-2-220000002-1-22-22-21-1-11-1-2112-11-11-111-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i300002i−2i00000000000000−33−33−ii−ii00000000
χ362-222-2-2-222-22-22-2-220000002-1-22-22-21-1-11-1-2112-11-11-111-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i30000−2i2i000000000000003−33−3i−ii−i00000000
χ372-22-2-222-22-22-2-222-22i−2i2i2i−2i−2i22-22-2-22-22-22-22-22-22-22-2-222-22i−2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ382-22-2-222-22-22-2-222-22i−2i2i2i−2i−2i2-1-22-2-221-11-1121-1-2-11-111-1-11−iii−i2i−2i2i−2i−ii−iii−ii−i000000000000000000003−3−33i3−i3−i3i300000000
χ392-22-2-222-22-22-2-222-22i−2i2i2i−2i−2i2-1-22-2-221-11-1121-1-2-11-111-1-11−iii−i2i−2i2i−2i−ii−iii−ii−i00000000000000000000−333−3−i3i3i3−i300000000
χ402-22-2-222-22-22-2-222-22i−2i2i2i−2i−2i-121-111-1-22-22-2-1-221-11-111-1-112i−2i−2i2i−ii−ii−ii−iii−ii−i0000000000000000000000000000−i3i3−i3i33−33−3
χ412-22-2-222-22-22-2-222-22i−2i2i2i−2i−2i-121-111-1-22-22-2-1-221-11-111-1-112i−2i−2i2i−ii−ii−ii−iii−ii−i0000000000000000000000000000i3−i3i3−i3−33−33
χ422-22-2-222-22-22-2-222-2−2i2i−2i−2i2i2i22-22-2-22-22-22-22-22-22-22-2-222-2−2i2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ432-22-2-222-22-22-2-222-2−2i2i−2i−2i2i2i2-1-22-2-221-11-1121-1-2-11-111-1-11i−i−ii−2i2i−2i2ii−ii−i−ii−ii000000000000000000003−3−33−i3i3i3−i300000000
χ442-22-2-222-22-22-2-222-2−2i2i−2i−2i2i2i2-1-22-2-221-11-1121-1-2-11-111-1-11i−i−ii−2i2i−2i2ii−ii−i−ii−ii00000000000000000000−333−3i3−i3−i3i300000000
χ452-22-2-222-22-22-2-222-2−2i2i−2i−2i2i2i-121-111-1-22-22-2-1-221-11-111-1-11−2i2i2i−2ii−ii−ii−ii−i−ii−ii0000000000000000000000000000−i3i3−i3i3−33−33
χ462-22-2-222-22-22-2-222-2−2i2i−2i−2i2i2i-121-111-1-22-22-2-1-221-11-111-1-11−2i2i2i−2ii−ii−ii−ii−i−ii−ii0000000000000000000000000000i3−i3i3−i33−33−3
χ472-2-222-22-22-2-2222-2-200000022-2-222-2-2-22-2-2222-22-2-222-22-2000000000000000000000000002i−2i000000000000000000002i−2i−2i2i
χ482-2-222-22-22-2-2222-2-200000022-2-222-2-2-22-2-2222-22-2-222-22-200000000000000000000000000−2i2i00000000000000000000−2i2i2i−2i
χ492-2-222-22-22-2-2222-2-2000000-1211-1-11-2-22-2-2-1221-111-1-11-1100003−3−333−3−33−333−300000000002i−2i0000000000000000−i3i3i3−i3−iii−i
χ502-2-222-22-22-2-2222-2-2000000-1211-1-11-2-22-2-2-1221-111-1-11-1100003−3−333−3−33−333−30000000000−2i2i0000000000000000i3−i3−i3i3i−i−ii
χ512-2-222-22-22-2-2222-2-2000000-1211-1-11-2-22-2-2-1221-111-1-11-110000−333−3−333−33−3−3300000000002i−2i0000000000000000i3−i3−i3i3−iii−i
χ522-2-222-22-22-2-2222-2-2000000-1211-1-11-2-22-2-2-1221-111-1-11-110000−333−3−333−33−3−330000000000−2i2i0000000000000000−i3i3i3−i3i−i−ii
χ532-2-2-222-222-2-22-2-22200000022-2-22-22-2-2-222-22-222-2-22-22-220000000000000000000000002-200000022-2-20000000000000000
χ542-2-2-222-222-2-22-2-22200000022-2-22-22-2-2-222-22-222-2-22-22-22000000000000000000000000-22000000-2-2220000000000000000
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
χ57444-44-4-4-44444-4-4-4-4000000-24-2-2-22244-4-4-424-42-2-2-2-222220000000000000000000000000000000000000000000000000000
χ58444-44-4-4-44444-4-4-4-4000000-2-2-2-2-222-2-22222-2221111-1-1-1-12323−23−230000−3−3−3−33333000000000000000000000000000000000000
χ59444-44-4-4-44444-4-4-4-4000000-2-2-2-2-222-2-22222-2221111-1-1-1-1−23−23232300003333−3−3−3−3000000000000000000000000000000000000
χ6044-44-44-4-444-4-44-44-40000004-24-4-444-22-2-22-422-4-2-222-2-2220000000000000000000000000000000000000000000000000000
χ6144-44-44-4-444-4-44-44-4000000-24-222-2-24-444-42-4-42-2-222-2-2220000000000000000000000000000000000000000000000000000
χ6244-44-44-4-444-4-44-44-4000000-2-2-222-2-2-22-2-22222211-1-111-1-1000000003i3i−3i−3i−3i−3i3i3i000000000000000000000000000000000000
χ6344-44-44-4-444-4-44-44-4000000-2-2-222-2-2-22-2-22222211-1-111-1-100000000−3i−3i3i3i3i3i−3i−3i000000000000000000000000000000000000
χ6444-4-4-4-44444-4-4-44-440000004-24-4-4-4-4-2222-242-24-2-22222-2-20000000000000000000000000000000000000000000000000000
χ6544-4-4-4-44444-4-4-44-44000000-2-2-22222-2222-2-22-2-211-1-1-1-1110000−2i3−2i32i32i3i3i3−i3−i3i3i3−i3−i3000000000000000000000000000000000000
χ6644-4-4-4-44444-4-4-44-44000000-2-2-22222-2222-2-22-2-211-1-1-1-11100002i32i3−2i3−2i3−i3−i3i3i3−i3−i3i3i3000000000000000000000000000000000000
χ674-444-4-4-444-44-44-4-44000000-242-22-22-444-442-4-4-2-22-22-222-20000000000000000000000000000000000000000000000000000
χ684-444-4-4-444-44-44-4-44000000-2-22-22-222-2-22-2222-21-11-11-1-11−2i32i3−2i32i30000i3−i3i3−i3i3−i3i3−i3000000000000000000000000000000000000
χ694-444-4-4-444-44-44-4-44000000-2-22-22-222-2-22-2222-21-11-11-1-112i3−2i32i3−2i30000−i3i3−i3i3−i3i3−i3i3000000000000000000000000000000000000
χ704-44-4-444-44-44-4-444-44i−4i4i4i−4i−4i-2-22-222-22-22-22-22-221-11-1-111-1−2i2i2i−2i−2i2i−2i2ii−ii−i−ii−ii000000000000000000000000000000000000
χ714-44-4-444-44-44-4-444-4−4i4i−4i−4i4i4i-2-22-222-22-22-22-22-221-11-1-111-12i−2i−2i2i2i−2i2i−2i−ii−iii−ii−i000000000000000000000000000000000000
χ724-4-444-44-44-4-4444-4-40000004-2-4-444-422-2224-2-2-4-222-2-22-220000000000000000000000000000000000000000000000000000
χ734-4-444-44-44-4-4444-4-4000000-2-222-2-2222-222-2-2-221-1-111-11-1000023−23−2323−333−33−3−33000000000000000000000000000000000000
χ744-4-444-44-44-4-4444-4-4000000-2-222-2-2222-222-2-2-221-1-111-11-10000−232323−233−3−33−333−3000000000000000000000000000000000000
χ754-4-4-444-444-4-44-4-4440000004-2-4-44-44222-2-2-4-224-222-22-22-20000000000000000000000000000000000000000000000000000
χ764-4-4-444-444-4-44-4-444000000-2422-22-2-4-4-44424-4-2-222-22-22-20000000000000000000000000000000000000000000000000000
χ774-4-4-444-444-4-44-4-444000000-2-222-22-2222-2-22-22-21-1-11-11-11000000003-3-333-3-33000000000000000000000000000000000000
χ784-4-4-444-444-4-44-4-444000000-2-222-22-2222-2-22-22-21-1-11-11-1100000000-333-3-333-3000000000000000000000000000000000000
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
χ8366-66-66-6-6-3-333-33-330033−3333−330000000000000000000000000000000000000000002-200000000-1-1113−33−30000000000000000
χ8466-66-66-6-6-3-333-33-330033−3333−33000000000000000000000000000000000000000000-220000000011-1-1−33−330000000000000000
χ8566-66-66-6-6-3-333-33-3300−3333−33330000000000000000000000000000000000000000002-200000000-1-111−33−330000000000000000
χ8666-66-66-6-6-3-333-33-3300−3333−3333000000000000000000000000000000000000000000-220000000011-1-13−33−30000000000000000
χ876-66-6-666-6-33-333-3-336i−6i−3i−3i3i3i0000000000000000000000000000000000000000000000000000−i3i3−i3i33−3−330000000000000000
χ886-66-6-666-6-33-333-3-336i−6i−3i−3i3i3i0000000000000000000000000000000000000000000000000000i3−i3i3−i3−333−30000000000000000
χ896-66-6-666-6-33-333-3-33−6i6i3i3i−3i−3i0000000000000000000000000000000000000000000000000000−i3i3−i3i3−333−30000000000000000
χ906-66-6-666-6-33-333-3-33−6i6i3i3i−3i−3i0000000000000000000000000000000000000000000000000000i3−i3i3−i33−3−330000000000000000
χ916-6-6-666-66-333-333-3-300−3i33i33i3−3i30000000000000000000000000000000000000000000000002-200−i3i3i3−i3-1-1110000000000000000
χ926-6-6-666-66-333-333-3-300−3i33i33i3−3i3000000000000000000000000000000000000000000000000-2200i3−i3−i3i311-1-10000000000000000
χ936-6-6-666-66-333-333-3-3003i3−3i3−3i33i30000000000000000000000000000000000000000000000002-200i3−i3−i3i3-1-1110000000000000000
χ946-6-6-666-66-333-333-3-3003i3−3i3−3i33i3000000000000000000000000000000000000000000000000-2200−i3i3i3−i311-1-10000000000000000
χ95121212-1212-12-12-12-6-6-6-666660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ961212-12-12-12-121212-6-6666-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-121212-12-12-1212-66-66-666-60000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12-121212-1212-12-666-6-6-6660000000000000000000000000000000000000000000000000000000000000000000000000000000000

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