Finite Group Databasebeta

← Group #13140169

Character table — Group #13140169

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order122222223666666644121212123366666666666666366666661212121212121212121212121212121222444444444466661212121212121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ922222222222222222222222-12222-1-1-1-1-12-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1220000002200-1-1-1-100000000-1-1-1-100000000
χ1022222222222222222222222-12222-1-1-1-1-12-122-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2000000-2-200111100000000111100000000
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
χ132222222222222222-2-2-2-2-2-22-12222-1-1-1-1-12-122-1-1-1-1-1-1-1-1-1-2-2-2-211111111111122000000-2-200-1-1-1-100000000111100000000
χ142222222222222222-2-2-2-2-2-22-12222-1-1-1-1-12-122-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111-2-20000002200111100000000-1-1-1-100000000
χ152222222222222222-2-2-2-2-2-2-12-1-1-1-122222-12-1-12-1-1-1-1-1-1-1-11111-2-2-2-2111111110000002200-2-20000000000000000-1-1-1-11111
χ162222222222222222-2-2-2-2-2-2-12-1-1-1-122222-12-1-12-1-1-1-1-1-1-1-11111-2-2-2-211111111000000-2-2002200000000000000001111-1-1-1-1
χ17222-2-2-2-222222-2-2-2-20000002222-2-222-2-2-2-2-22-222222-2-2-2-200000000000000000000002i−2i000000000000000000002i2i−2i−2i0000
χ18222-2-2-2-222222-2-2-2-20000002222-2-222-2-2-2-2-22-222222-2-2-2-20000000000000000000000−2i2i00000000000000000000−2i−2i2i2i0000
χ19222-2-2-2-222222-2-2-2-2000000-12-1-11122-2-2-21-2-112-1-1-1-1111133−3−300003333−3−3−3−30000002i−2i00000000000000000000−i−iii−i3−i3i3i3
χ20222-2-2-2-222222-2-2-2-2000000-12-1-11122-2-2-21-2-112-1-1-1-1111133−3−300003333−3−3−3−3000000−2i2i00000000000000000000ii−i−ii3i3−i3−i3
χ21222-2-2-2-222222-2-2-2-2000000-12-1-11122-2-2-21-2-112-1-1-1-11111−3−3330000−3−3−3−333330000002i−2i00000000000000000000−i−iiii3i3−i3−i3
χ22222-2-2-2-222222-2-2-2-2000000-12-1-11122-2-2-21-2-112-1-1-1-11111−3−3330000−3−3−3−33333000000−2i2i00000000000000000000ii−i−i−i3−i3i3i3
χ2322-222-2-2-222-2-222-2-2000000222-2-2-22-22-2-222-22-222-2-22-2-22000000000000000000002i−2i000000000000002i2i−2i−2i000000000000
χ2422-222-2-2-222-2-222-2-2000000222-2-2-22-22-2-222-22-222-2-22-2-2200000000000000000000−2i2i00000000000000−2i−2i2i2i000000000000
χ2522-2-2-222-222-2-2-2-222000000222-2222-2-222-2-2-2-2-222-2-2-222-20000000000000000000000002i−2i000000000000002i2i−2i−2i00000000
χ2622-2-2-222-222-2-2-2-222000000222-2222-2-222-2-2-2-2-222-2-2-222-2000000000000000000000000−2i2i00000000000000−2i−2i2i2i00000000
χ2722-2-2-222-222-2-2-2-2220000002-12-222-111-1-1-21-2-21-1-1111-1-11000033−3−333−3−333−3−3000000002i−2i00−i3−i3i3i300000000−i−iii00000000
χ2822-2-2-222-222-2-2-2-2220000002-12-222-111-1-1-21-2-21-1-1111-1-11000033−3−333−3−333−3−300000000−2i2i00i3i3−i3−i300000000ii−i−i00000000
χ2922-2-2-222-222-2-2-2-2220000002-12-222-111-1-1-21-2-21-1-1111-1-110000−3−333−3−333−3−333000000002i−2i00i3i3−i3−i300000000−i−iii00000000
χ3022-2-2-222-222-2-2-2-2220000002-12-222-111-1-1-21-2-21-1-1111-1-110000−3−333−3−333−3−33300000000−2i2i00−i3−i3i3i300000000ii−i−i00000000
χ312-222-22-2-22-22-2-222-200000022-222-2-22-22-222-2-2-22-22-2-22-22000000000000000000000000002i−2i000000000000000000002i−2i2i−2i
χ322-222-22-2-22-22-2-222-200000022-222-2-22-22-222-2-2-22-22-2-22-2200000000000000000000000000−2i2i00000000000000000000−2i2i−2i2i
χ332-222-22-2-22-22-2-222-2000000-121-1-11-22-22-2-1211-2-11-111-11-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i300000000002i−2i00000000000000003−33−3−ii−ii
χ342-222-22-2-22-22-2-222-2000000-121-1-11-22-22-2-1211-2-11-111-11-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i30000000000−2i2i0000000000000000−33−33i−ii−i
χ352-222-22-2-22-22-2-222-2000000-121-1-11-22-22-2-1211-2-11-111-11-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i300000000002i−2i0000000000000000−33−33−ii−ii
χ362-222-22-2-22-22-2-222-2000000-121-1-11-22-22-2-1211-2-11-111-11-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i30000000000−2i2i00000000000000003−33−3i−ii−i
χ372-22-22-22-22-22-22-2-222i−2i2i2i−2i−2i22-22-22-222-22-2-2-22-22-22-22-22-22i−2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000
χ382-22-22-22-22-22-22-2-222i−2i2i2i−2i−2i2-1-22-221-1-11-1-21-221-11-11-11-112i−2i−2i2i−ii−ii−ii−iii−ii−i000000000000−i3i3−i3i3000000003−33−300000000
χ392-22-22-22-22-22-22-2-222i−2i2i2i−2i−2i2-1-22-221-1-11-1-21-221-11-11-11-112i−2i−2i2i−ii−ii−ii−iii−ii−i000000000000i3−i3i3−i300000000−33−3300000000
χ402-22-22-22-22-22-22-2-222i−2i2i2i−2i−2i-121-11-1-222-221-21-1-2-11-11-11-11−iii−i2i−2i2i−2i−ii−iii−ii−i0000000000000000000000000000−i3i3i3−i3−333−3
χ412-22-22-22-22-22-22-2-222i−2i2i2i−2i−2i-121-11-1-222-221-21-1-2-11-11-11-11−iii−i2i−2i2i−2i−ii−iii−ii−i0000000000000000000000000000i3−i3−i3i33−3−33
χ422-22-22-22-22-22-22-2-22−2i2i−2i−2i2i2i22-22-22-222-22-2-2-22-22-22-22-22-2−2i2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000
χ432-22-22-22-22-22-22-2-22−2i2i−2i−2i2i2i2-1-22-221-1-11-1-21-221-11-11-11-11−2i2i2i−2ii−ii−ii−ii−i−ii−ii000000000000−i3i3−i3i300000000−33−3300000000
χ442-22-22-22-22-22-22-2-22−2i2i−2i−2i2i2i2-1-22-221-1-11-1-21-221-11-11-11-11−2i2i2i−2ii−ii−ii−ii−i−ii−ii000000000000i3−i3i3−i3000000003−33−300000000
χ452-22-22-22-22-22-22-2-22−2i2i−2i−2i2i2i-121-11-1-222-221-21-1-2-11-11-11-11i−i−ii−2i2i−2i2ii−ii−i−ii−ii0000000000000000000000000000−i3i3i3−i33−3−33
χ462-22-22-22-22-22-22-2-22−2i2i−2i−2i2i2i-121-11-1-222-221-21-1-2-11-11-11-11i−i−ii−2i2i−2i2ii−ii−i−ii−ii0000000000000000000000000000i3−i3−i3i3−333−3
χ472-2-22-2-2222-2-22-22-2200000022-2-2-22-2-2-2-22222-222-2-22-2-22200000000000000002-200000000002-2-2200000000000000000000
χ482-2-22-2-2222-2-22-22-2200000022-2-2-22-2-2-2-22222-222-2-22-2-2220000000000000000-220000000000-222-200000000000000000000
χ492-2-22-2-2222-2-22-22-220000002-1-2-2-221111-12-12-2-1-111-111-1-10000−i3i3i3−i3−i3i3i3−i3i3−i3−i3i32-20000000000-111-100000000−i3i3i3−i300000000
χ502-2-22-2-2222-2-22-22-220000002-1-2-2-221111-12-12-2-1-111-111-1-10000−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3-2200000000001-1-1100000000i3−i3−i3i300000000
χ512-2-22-2-2222-2-22-22-220000002-1-2-2-221111-12-12-2-1-111-111-1-10000i3−i3−i3i3i3−i3−i3i3−i3i3i3−i32-20000000000-111-100000000i3−i3−i3i300000000
χ522-2-22-2-2222-2-22-22-220000002-1-2-2-221111-12-12-2-1-111-111-1-10000i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3-2200000000001-1-1100000000−i3i3i3−i300000000
χ532-2-2-222-222-2-222-22-200000022-2-22-2-2-222-2-2-22222-2-2222-2-20000000000000000002-200000000000022-2-20000000000000000
χ542-2-2-222-222-2-222-22-200000022-2-22-2-2-222-2-2-22222-2-2222-2-2000000000000000000-22000000000000-2-2220000000000000000
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
χ57444-4-4-4-444444-4-4-4-40000004-244-4-4-2-2222-424-4-2-2-2-2-222220000000000000000000000000000000000000000000000000000
χ58444-4-4-4-444444-4-4-4-4000000-2-2-2-222-2-222222-22-21111-1-1-1-12323−23−230000−3−3−3−33333000000000000000000000000000000000000
χ59444-4-4-4-444444-4-4-4-4000000-2-2-2-222-2-222222-22-21111-1-1-1-1−23−23232300003333−3−3−3−3000000000000000000000000000000000000
χ6044-444-4-4-444-4-444-4-40000004-24-4-4-4-22-2224-2-442-2-222-222-20000000000000000000000000000000000000000000000000000
χ6144-444-4-4-444-4-444-4-4000000-24-22224-44-4-4-242-2-4-2-222-222-20000000000000000000000000000000000000000000000000000
χ6244-444-4-4-444-4-444-4-4000000-2-2-2222-22-222-2-22-2211-1-11-1-110000000033-3-3-3-333000000000000000000000000000000000000
χ6344-444-4-4-444-4-444-4-4000000-2-2-2222-22-222-2-22-2211-1-11-1-1100000000-3-33333-3-3000000000000000000000000000000000000
χ6444-4-4-444-444-4-4-4-444000000-24-22-2-24-4-4442-422-4-2-2222-2-220000000000000000000000000000000000000000000000000000
χ6544-4-4-444-444-4-4-4-444000000-2-2-22-2-2-222-2-22222211-1-1-111-100002323−23−23−3−333−3−333000000000000000000000000000000000000
χ6644-4-4-444-444-4-4-4-444000000-2-2-22-2-2-222-2-22222211-1-1-111-10000−23−23232333−3−333−3−3000000000000000000000000000000000000
χ674-444-44-4-44-44-4-444-40000004-2-444-42-22-224-2-4-42-22-222-22-20000000000000000000000000000000000000000000000000000
χ684-444-44-4-44-44-4-444-4000000-2-22-2-222-22-22-2-22221-11-1-11-11−2i32i3−2i32i30000i3−i3i3−i3i3−i3i3−i3000000000000000000000000000000000000
χ694-444-44-4-44-44-4-444-4000000-2-22-2-222-22-22-2-22221-11-1-11-112i3−2i32i3−2i30000−i3i3−i3i3−i3i3−i3i3000000000000000000000000000000000000
χ704-44-44-44-44-44-44-4-444i−4i4i4i−4i−4i-2-22-22-22-2-22-2222-221-11-11-11-1−2i2i2i−2i−2i2i−2i2ii−ii−i−ii−ii000000000000000000000000000000000000
χ714-44-44-44-44-44-44-4-44−4i4i−4i−4i4i4i-2-22-22-22-2-22-2222-221-11-11-11-12i−2i−2i2i2i−2i2i−2i−ii−iii−ii−i000000000000000000000000000000000000
χ724-4-44-4-4444-4-44-44-44000000-24222-2-4-4-4-44-24-224-222-222-2-20000000000000000000000000000000000000000000000000000
χ734-4-44-4-4444-4-44-44-44000000-2-2222-22222-2-2-2-22-21-1-11-1-1110000−2i32i32i3−2i3i3−i3−i3i3−i3i3i3−i3000000000000000000000000000000000000
χ744-4-44-4-4444-4-44-44-44000000-2-2222-22222-2-2-2-22-21-1-11-1-11100002i3−2i3−2i32i3−i3i3i3−i3i3−i3−i3i3000000000000000000000000000000000000
χ754-4-4-444-444-4-444-44-40000004-2-4-44-422-2-22-4244-2-222-2-2-2220000000000000000000000000000000000000000000000000000
χ764-4-4-444-444-4-444-44-4000000-2422-22-4-444-42-4-2-24-222-2-2-2220000000000000000000000000000000000000000000000000000
χ774-4-4-444-444-4-444-44-4000000-2-222-2222-2-2222-2-2-21-1-1111-1-1000000003i−3i−3i3i3i−3i−3i3i000000000000000000000000000000000000
χ784-4-4-444-444-4-444-44-4000000-2-222-2222-2-2222-2-2-21-1-1111-1-100000000−3i3i3i−3i−3i3i3i−3i000000000000000000000000000000000000
χ7966666666-3-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000000000022220000000000-1-1-1-1-1-1-1-1000000000000
χ8066666666-3-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000000000-2-2-2-2000000000011111111000000000000
χ8166666666-3-3-3-3-3-3-3-3-6-6333300000000000000000000000000000000000000000022-2-20000000000-1-1-1-11111000000000000
χ8266666666-3-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000000000-2-22200000000001111-1-1-1-1000000000000
χ8366-666-6-6-6-3-333-3-33300−3i33i3−3i33i3000000000000000000000000000000000000000000002i−2i00000000003−33−3−i−iii000000000000
χ8466-666-6-6-6-3-333-3-33300−3i33i3−3i33i300000000000000000000000000000000000000000000−2i2i0000000000−33−33ii−i−i000000000000
χ8566-666-6-6-6-3-333-3-333003i3−3i33i3−3i3000000000000000000000000000000000000000000002i−2i0000000000−33−33−i−iii000000000000
χ8666-666-6-6-6-3-333-3-333003i3−3i33i3−3i300000000000000000000000000000000000000000000−2i2i00000000003−33−3ii−i−i000000000000
χ876-66-66-66-6-33-33-333-36i−6i−3i−3i3i3i000000000000000000000000000000000000000000000000000000003−3−33−i3i3−i3i3000000000000
χ886-66-66-66-6-33-33-333-36i−6i−3i−3i3i3i00000000000000000000000000000000000000000000000000000000−333−3i3−i3i3−i3000000000000
χ896-66-66-66-6-33-33-333-3−6i6i3i3i−3i−3i000000000000000000000000000000000000000000000000000000003−3−33i3−i3i3−i3000000000000
χ906-66-66-66-6-33-33-333-3−6i6i3i3i−3i−3i00000000000000000000000000000000000000000000000000000000−333−3−i3i3−i3i3000000000000
χ916-6-6-666-66-333-3-33-330033−33−33330000000000000000000000000000000000000000002-2000000000000-1-111−333−3000000000000
χ926-6-6-666-66-333-3-33-330033−33−3333000000000000000000000000000000000000000000-2200000000000011-1-13−3−33000000000000
χ936-6-6-666-66-333-3-33-3300−333333−330000000000000000000000000000000000000000002-2000000000000-1-1113−3−33000000000000
χ946-6-6-666-66-333-3-33-3300−333333−33000000000000000000000000000000000000000000-2200000000000011-1-1−333−3000000000000
χ95121212-12-12-12-1212-6-6-6-666660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ961212-12-12-121212-12-6-66666-6-60000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-121212-1212-12-12-66-666-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12-1212-12-121212-666-66-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000

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