Finite Group Databasebeta

← Group #13140117

Character table — Group #13140117

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order122222223666666644121212123366666666666666366666661212121212121212121212121212121222444444444466661212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ922222222222222222222222-12222-1-1-1-1-12-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1222200000000-1-1-1-100000000-1-1-1-100000000
χ1022222222222222222222222-12222-1-1-1-1-12-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000111100000000111100000000
χ112222222222222222222222-12-1-1-1-122222-12-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000002200220000000000000000-1-1-1-1-1-1-1-1
χ122222222222222222222222-12-1-1-1-122222-12-1-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000-2-200-2-2000000000000000011111111
χ132222222222222222-2-2-2-2-2-22-12222-1-1-1-1-12-122-1-1-1-1-1-1-1-1-1-2-2-2-211111111111122-2-200000000-1-1-1-100000000111100000000
χ142222222222222222-2-2-2-2-2-22-12222-1-1-1-1-12-122-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111-2-22200000000111100000000-1-1-1-100000000
χ152222222222222222-2-2-2-2-2-2-12-1-1-1-122222-12-1-12-1-1-1-1-1-1-1-11111-2-2-2-2111111110000002200-2-200000000000000001111-1-1-1-1
χ162222222222222222-2-2-2-2-2-2-12-1-1-1-122222-12-1-12-1-1-1-1-1-1-1-11111-2-2-2-211111111000000-2-200220000000000000000-1-1-1-11111
χ17222-2-2-2-22222-2-2-22-22i−2i2i2i−2i−2i2222-2-2222-2-2-2-22-2-22222-2-2-2-22i2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ18222-2-2-2-22222-2-2-22-22i−2i2i2i−2i−2i2-122-2-2-1-1-111-212-21-1-1-1-111112i2i−2i−2i−i−iii−i−i−i−iiiii000000000000−i3−i3i3i30000000033−3−300000000
χ19222-2-2-2-22222-2-2-22-22i−2i2i2i−2i−2i2-122-2-2-1-1-111-212-21-1-1-1-111112i2i−2i−2i−i−iii−i−i−i−iiiii000000000000i3i3−i3−i300000000−3−33300000000
χ20222-2-2-2-22222-2-2-22-22i−2i2i2i−2i−2i-12-1-111222-2-21-2-11-2-1-1-1-11111−i−iii2i2i−2i−2i−i−i−i−iiiii0000000000000000000000000000−i3−i3i3i333−3−3
χ21222-2-2-2-22222-2-2-22-22i−2i2i2i−2i−2i-12-1-111222-2-21-2-11-2-1-1-1-11111−i−iii2i2i−2i−2i−i−i−i−iiiii0000000000000000000000000000i3i3−i3−i3−3−333
χ22222-2-2-2-22222-2-2-22-2−2i2i−2i−2i2i2i2222-2-2222-2-2-2-22-2-22222-2-2-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ23222-2-2-2-22222-2-2-22-2−2i2i−2i−2i2i2i2-122-2-2-1-1-111-212-21-1-1-1-11111−2i−2i2i2iii−i−iiiii−i−i−i−i000000000000−i3−i3i3i300000000−3−33300000000
χ24222-2-2-2-22222-2-2-22-2−2i2i−2i−2i2i2i2-122-2-2-1-1-111-212-21-1-1-1-11111−2i−2i2i2iii−i−iiiii−i−i−i−i000000000000i3i3−i3−i30000000033−3−300000000
χ25222-2-2-2-22222-2-2-22-2−2i2i−2i−2i2i2i-12-1-111222-2-21-2-11-2-1-1-1-11111ii−i−i−2i−2i2i2iiiii−i−i−i−i0000000000000000000000000000−i3−i3i3i3−3−333
χ26222-2-2-2-22222-2-2-22-2−2i2i−2i−2i2i2i-12-1-111222-2-21-2-11-2-1-1-1-11111ii−i−i−2i−2i2i2iiiii−i−i−i−i0000000000000000000000000000i3i3−i3−i333−3−3
χ2722-222-2-2-222-22-22-2-2000000222-2-2-22-2-22-222-22-222-2-22-2-22000000000000000000002i−2i00000000002i2i−2i−2i0000000000000000
χ2822-222-2-2-222-22-22-2-2000000222-2-2-22-2-22-222-22-222-2-22-2-2200000000000000000000−2i2i0000000000−2i−2i2i2i0000000000000000
χ2922-2-2-222-222-2-22-2-22000000222-2222-2-2-22-2-2-2-2222-2-2-222-20000000000000000000000002i−2i00000000002i2i−2i−2i000000000000
χ3022-2-2-222-222-2-22-2-22000000222-2222-2-2-22-2-2-2-2222-2-2-222-2000000000000000000000000−2i2i0000000000−2i−2i2i2i000000000000
χ312-222-22-2-22-22-2-22-2200000022-222-2-22-2-2222-2-2-22-22-2-22-2200000000000000000000002i−2i0000000000000000000000002i−2i2i−2i
χ322-222-22-2-22-22-2-22-2200000022-222-2-22-2-2222-2-2-22-22-2-22-220000000000000000000000−2i2i000000000000000000000000−2i2i−2i2i
χ332-222-22-2-22-22-2-22-22000000-121-1-11-22-2-22-1211-2-11-111-11-1−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i30000002i−2i000000000000000000003−33−3−ii−ii
χ342-222-22-2-22-22-2-22-22000000-121-1-11-22-2-22-1211-2-11-111-11-1−i3i3−i3i30000−i3−i3i3i3−i3−i3i3i3000000−2i2i00000000000000000000−33−33i−ii−i
χ352-222-22-2-22-22-2-22-22000000-121-1-11-22-2-22-1211-2-11-111-11-1i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i30000002i−2i00000000000000000000−33−33−ii−ii
χ362-222-22-2-22-22-2-22-22000000-121-1-11-22-2-22-1211-2-11-111-11-1i3−i3i3−i30000i3i3−i3−i3i3i3−i3−i3000000−2i2i000000000000000000003−33−3i−ii−i
χ372-22-22-22-22-2222-2-2-200000022-22-22-22-22-2-2-2-2222-22-22-22-2000000000000000000000000002i−2i00000000000000002i−2i−2i2i0000
χ382-22-22-22-22-2222-2-2-200000022-22-22-22-22-2-2-2-2222-22-22-22-200000000000000000000000000−2i2i0000000000000000−2i2i2i−2i0000
χ392-22-22-22-22-2222-2-2-2000000-121-11-1-22-22-21-21-12-11-11-11-113−3−33000033−3−3−3−33300000000002i−2i0000000000000000−iii−ii3−i3−i3i3
χ402-22-22-22-22-2222-2-2-2000000-121-11-1-22-22-21-21-12-11-11-11-113−3−33000033−3−3−3−3330000000000−2i2i0000000000000000i−i−ii−i3i3i3−i3
χ412-22-22-22-22-2222-2-2-2000000-121-11-1-22-22-21-21-12-11-11-11-11−333−30000−3−33333−3−300000000002i−2i0000000000000000−iii−i−i3i3i3−i3
χ422-22-22-22-22-2222-2-2-2000000-121-11-1-22-22-21-21-12-11-11-11-11−333−30000−3−33333−3−30000000000−2i2i0000000000000000i−i−iii3−i3−i3i3
χ432-2-22-2-2222-2-2-2222-200000022-2-2-22-2-22-2-2222-222-2-22-2-2220000000000000000002-2000000000000000000002-22-200000000
χ442-2-22-2-2222-2-2-2222-200000022-2-2-22-2-22-2-2222-222-2-22-2-222000000000000000000-2200000000000000000000-22-2200000000
χ452-2-22-2-2222-2-2-2222-20000002-1-2-2-2211-1112-12-2-1-111-111-1-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3002-200000000−i3i3−i3i300000000-11-1100000000
χ462-2-22-2-2222-2-2-2222-20000002-1-2-2-2211-1112-12-2-1-111-111-1-10000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i300-2200000000i3−i3i3−i3000000001-11-100000000
χ472-2-22-2-2222-2-2-2222-20000002-1-2-2-2211-1112-12-2-1-111-111-1-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3002-200000000i3−i3i3−i300000000-11-1100000000
χ482-2-22-2-2222-2-2-2222-20000002-1-2-2-2211-1112-12-2-1-111-111-1-10000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i300-2200000000−i3i3−i3i3000000001-11-100000000
χ492-2-2-222-222-2-22-2-22200000022-2-22-2-2-2222-2-222-22-2-2222-2-200000000000000002-200000000002-2-2200000000000000000000
χ502-2-2-222-222-2-22-2-22200000022-2-22-2-2-2222-2-222-22-2-2222-2-20000000000000000-220000000000-222-200000000000000000000
χ512-2-2-222-222-2-22-2-2220000002-1-2-22-211-1-1-1-21221-111-1-1-11100003−3−333−33−3−33−332-20000000000-111-1000000003−3−3300000000
χ522-2-2-222-222-2-22-2-2220000002-1-2-22-211-1-1-1-21221-111-1-1-11100003−3−333−33−3−33−33-2200000000001-1-1100000000−333−300000000
χ532-2-2-222-222-2-22-2-2220000002-1-2-22-211-1-1-1-21221-111-1-1-1110000−333−3−33−333−33−32-20000000000-111-100000000−333−300000000
χ542-2-2-222-222-2-22-2-2220000002-1-2-22-211-1-1-1-21221-111-1-1-1110000−333−3−33−333−33−3-2200000000001-1-11000000003−3−3300000000
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
χ57444-4-4-4-44444-4-4-44-44i−4i4i4i−4i−4i-2-2-2-222-2-2-22222-2221111-1-1-1-1−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−i000000000000000000000000000000000000
χ58444-4-4-4-44444-4-4-44-4−4i4i−4i−4i4i4i-2-2-2-222-2-2-22222-2221111-1-1-1-12i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii000000000000000000000000000000000000
χ5944-444-4-4-444-44-44-4-40000004-24-4-4-4-222-224-2-442-2-222-222-20000000000000000000000000000000000000000000000000000
χ6044-444-4-4-444-44-44-4-4000000-24-22224-4-44-4-242-2-4-2-222-222-20000000000000000000000000000000000000000000000000000
χ6144-444-4-4-444-44-44-4-4000000-2-2-2222-222-22-2-22-2211-1-11-1-11000000003-3-333-3-33000000000000000000000000000000000000
χ6244-444-4-4-444-44-44-4-4000000-2-2-2222-222-22-2-22-2211-1-11-1-1100000000-333-3-333-3000000000000000000000000000000000000
χ6344-4-4-444-444-4-44-4-440000004-24-444-2222-2-42-4-4-2-2-2222-2-220000000000000000000000000000000000000000000000000000
χ6444-4-4-444-444-4-44-4-44000000-24-22-2-24-4-4-442-4224-2-2222-2-220000000000000000000000000000000000000000000000000000
χ6544-4-4-444-444-4-44-4-44000000-2-2-22-2-2-2222-22222-211-1-1-111-1000000003i−3i−3i3i−3i3i3i−3i000000000000000000000000000000000000
χ6644-4-4-444-444-4-44-4-44000000-2-2-22-2-2-2222-22222-211-1-1-111-100000000−3i3i3i−3i3i−3i−3i3i000000000000000000000000000000000000
χ674-444-44-4-44-44-4-44-440000004-2-444-42-222-24-2-4-42-22-222-22-20000000000000000000000000000000000000000000000000000
χ684-444-44-4-44-44-4-44-44000000-2-22-2-222-222-2-2-22221-11-1-11-11−2i32i3−2i32i30000i3i3−i3−i3i3i3−i3−i3000000000000000000000000000000000000
χ694-444-44-4-44-44-4-44-44000000-2-22-2-222-222-2-2-22221-11-1-11-112i3−2i32i3−2i30000−i3−i3i3i3−i3−i3i3i3000000000000000000000000000000000000
χ704-44-44-44-44-4444-4-4-40000004-2-44-442-22-22-42-44-2-22-22-22-220000000000000000000000000000000000000000000000000000
χ714-44-44-44-44-4444-4-4-4000000-2-22-22-22-22-22222-2-21-11-11-11-123−23−23230000−3−33333−3−3000000000000000000000000000000000000
χ724-44-44-44-44-4444-4-4-4000000-2-22-22-22-22-22222-2-21-11-11-11-1−232323−23000033−3−3−3−333000000000000000000000000000000000000
χ734-4-44-4-4444-4-4-4444-4000000-24222-2-4-44-4-4-24-224-222-222-2-20000000000000000000000000000000000000000000000000000
χ744-4-44-4-4444-4-4-4444-4000000-2-2222-222-222-2-2-22-21-1-11-1-1110000−2i32i3−2i32i3i3−i3i3−i3i3−i3i3−i3000000000000000000000000000000000000
χ754-4-44-4-4444-4-4-4444-4000000-2-2222-222-222-2-2-22-21-1-11-1-11100002i3−2i32i3−2i3−i3i3−i3i3−i3i3−i3i3000000000000000000000000000000000000
χ764-4-4-444-444-4-44-4-444000000-2422-22-4-44442-4-2-2-4-222-2-2-2220000000000000000000000000000000000000000000000000000
χ774-4-4-444-444-4-44-4-444000000-2-222-2222-2-2-222-2-221-1-1111-1-1000023−23−2323−33−333−33−3000000000000000000000000000000000000
χ784-4-4-444-444-4-44-4-444000000-2-222-2222-2-2-222-2-221-1-1111-1-10000−232323−233−33−3−33−33000000000000000000000000000000000000
χ7966666666-3-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000000000000220022000000-1-1-1-1-1-1-1-1000000000000
χ8066666666-3-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000000000000-2-200-2-200000011111111000000000000
χ8166666666-3-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000000000002200-2-2000000-1-1-1-11111000000000000
χ8266666666-3-3-3-3-3-3-3-3-6-6333300000000000000000000000000000000000000000000-2-200220000001111-1-1-1-1000000000000
χ83666-6-6-6-66-3-3-3333-336i−6i−3i−3i3i3i000000000000000000000000000000000000000000000000000000003−33−3−i3i3−i3i3000000000000
χ84666-6-6-6-66-3-3-3333-336i−6i−3i−3i3i3i00000000000000000000000000000000000000000000000000000000−33−33i3−i3i3−i3000000000000
χ85666-6-6-6-66-3-3-3333-33−6i6i3i3i−3i−3i000000000000000000000000000000000000000000000000000000003−33−3i3−i3i3−i3000000000000
χ86666-6-6-6-66-3-3-3333-33−6i6i3i3i−3i−3i00000000000000000000000000000000000000000000000000000000−33−33−i3i3−i3i3000000000000
χ8766-666-6-6-6-3-33-33-33300−3i33i3−3i33i3000000000000000000000000000000000000000000002i−2i0000000000−i−iii3−3−33000000000000
χ8866-666-6-6-6-3-33-33-33300−3i33i3−3i33i300000000000000000000000000000000000000000000−2i2i0000000000ii−i−i−333−3000000000000
χ8966-666-6-6-6-3-33-33-333003i3−3i33i3−3i3000000000000000000000000000000000000000000002i−2i0000000000−i−iii−333−3000000000000
χ9066-666-6-6-6-3-33-33-333003i3−3i33i3−3i300000000000000000000000000000000000000000000−2i2i0000000000ii−i−i3−3−33000000000000
χ9166-6-6-666-6-3-333-333-30033−33−33330000000000000000000000000000000000000000000000002i−2i000000i3−i3−i3i3−i−iii000000000000
χ9266-6-6-666-6-3-333-333-30033−33−3333000000000000000000000000000000000000000000000000−2i2i000000−i3i3i3−i3ii−i−i000000000000
χ9366-6-6-666-6-3-333-333-300−333333−330000000000000000000000000000000000000000000000002i−2i000000−i3i3i3−i3−i−iii000000000000
χ9466-6-6-666-6-3-333-333-300−333333−33000000000000000000000000000000000000000000000000−2i2i000000i3−i3−i3i3ii−i−i000000000000
χ9512-121212-1212-12-12-66-666-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9612-1212-1212-1212-12-66-6-6-66660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-12-1212-12-121212-6666-6-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12-12-121212-1212-666-666-6-60000000000000000000000000000000000000000000000000000000000000000000000000000000000

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