Finite Group Databasebeta

← Group #13140178

Character table — Group #13140178

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
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ922222222222222222222222-122222-1-1-1-1-12-1-12-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1222200000000-1-1-1-100000000-1-1-1-100000000
χ1022222222222222222222222-122222-1-1-1-1-12-1-12-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000111100000000111100000000
χ112222222222222222222222-12-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000022220000000000000000-1-1-1-1-1-1-1-1
χ122222222222222222222222-12-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000-2-2-2-2000000000000000011111111
χ132222222222222222-2-2-2-2-2-22-122222-1-1-1-1-12-1-12-1-1-1-1-1-1-1-1-2-2-2-211111111111122-2-200000000-1-1-1-100000000111100000000
χ142222222222222222-2-2-2-2-2-22-122222-1-1-1-1-12-1-12-1-1-1-1-1-1-1-1-2-2-2-2111111111111-2-22200000000111100000000-1-1-1-100000000
χ152222222222222222-2-2-2-2-2-2-12-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-11111-2-2-2-2111111110000000022-2-20000000000000000-1-1-1-11111
χ162222222222222222-2-2-2-2-2-2-12-1-1-1-1-122222-122-1-1-1-1-1-1-1-1-11111-2-2-2-21111111100000000-2-22200000000000000001111-1-1-1-1
χ17222-2-2-2-222222-2-2-2-20000002222-2-2-2222-2-2-2-2-222222-2-2-2-20000000000000000002i−2i000000000000000000002i2i−2i−2i00000000
χ18222-2-2-2-222222-2-2-2-20000002222-2-2-2222-2-2-2-2-222222-2-2-2-2000000000000000000−2i2i00000000000000000000−2i−2i2i2i00000000
χ19222-2-2-2-222222-2-2-2-20000002-122-2-2-2-1-1-111-2112-1-1-1-11111000033−3−33333−3−3−3−3002i−2i00000000−i3−i3i3i300000000−i−iii00000000
χ20222-2-2-2-222222-2-2-2-20000002-122-2-2-2-1-1-111-2112-1-1-1-11111000033−3−33333−3−3−3−300−2i2i00000000i3i3−i3−i300000000ii−i−i00000000
χ21222-2-2-2-222222-2-2-2-20000002-122-2-2-2-1-1-111-2112-1-1-1-111110000−3−333−3−3−3−33333002i−2i00000000i3i3−i3−i300000000−i−iii00000000
χ22222-2-2-2-222222-2-2-2-20000002-122-2-2-2-1-1-111-2112-1-1-1-111110000−3−333−3−3−3−3333300−2i2i00000000−i3−i3i3i300000000ii−i−i00000000
χ2322-222-2-2-222-2-2-222-2000000222-22-2-22-2-22-222-2-222-2-22-2-22000000000000000000000000002i−2i000000000000000000002i2i−2i−2i
χ2422-222-2-2-222-2-2-222-2000000222-22-2-22-2-22-222-2-222-2-22-2-2200000000000000000000000000−2i2i00000000000000000000−2i−2i2i2i
χ2522-222-2-2-222-2-2-222-2000000-12-11-1112-2-22-2-12-21-1-111-111-1−i3−i3i3i30000−i3−i3i3i3−i3−i3i3i300000000002i−2i000000000000000033−3−3−i−iii
χ2622-222-2-2-222-2-2-222-2000000-12-11-1112-2-22-2-12-21-1-111-111-1−i3−i3i3i30000−i3−i3i3i3−i3−i3i3i30000000000−2i2i0000000000000000−3−333ii−i−i
χ2722-222-2-2-222-2-2-222-2000000-12-11-1112-2-22-2-12-21-1-111-111-1i3i3−i3−i30000i3i3−i3−i3i3i3−i3−i300000000002i−2i0000000000000000−3−333−i−iii
χ2822-222-2-2-222-2-2-222-2000000-12-11-1112-2-22-2-12-21-1-111-111-1i3i3−i3−i30000i3i3−i3−i3i3i3−i3−i30000000000−2i2i000000000000000033−3−3ii−i−i
χ2922-2-2-222-222-2-22-2-22000000222-2-2222-2-2-22-2-22-222-2-2-222-2000000000000000000002i−2i00000000002i2i−2i−2i0000000000000000
χ3022-2-2-222-222-2-22-2-22000000222-2-2222-2-2-22-2-22-222-2-2-222-200000000000000000000−2i2i0000000000−2i−2i2i2i0000000000000000
χ312-222-22-2-22-22-2-22-2200000022-22-22-2-22-2-2222-2-22-22-2-22-220000000000000000000000002i−2i0000000000000000002i−2i2i−2i0000
χ322-222-22-2-22-22-2-22-2200000022-22-22-2-22-2-2222-2-22-22-2-22-22000000000000000000000000−2i2i000000000000000000−2i2i−2i2i0000
χ332-222-22-2-22-22-2-22-22000000-121-11-11-22-2-22-12-21-11-111-11-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i3000000002i−2i000000000000000000−ii−ii3−33−3
χ342-222-22-2-22-22-2-22-22000000-121-11-11-22-2-22-12-21-11-111-11-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i300000000−2i2i000000000000000000i−ii−i−33−33
χ352-222-22-2-22-22-2-22-22000000-121-11-11-22-2-22-12-21-11-111-11-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i3000000002i−2i000000000000000000−ii−ii−33−33
χ362-222-22-2-22-22-2-22-22000000-121-11-11-22-2-22-12-21-11-111-11-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i300000000−2i2i000000000000000000i−ii−i3−33−3
χ372-22-22-22-22-22-22-22-200000022-222-22-22-22-2-2-22-22-22-22-22-200000000000000000000002i−2i0000000000002i2i−2i−2i000000000000
χ382-22-22-22-22-22-22-22-200000022-222-22-22-22-2-2-22-22-22-22-22-20000000000000000000000−2i2i000000000000−2i−2i2i2i000000000000
χ392-2-22-2-2222-2-2222-2-22-222-2-222-2-2-2-22-2-22-2-222222-2-22-2-2222-2-222-22-22-2-222-2-22000000000000000000000000000000000000
χ402-2-22-2-2222-2-2222-2-22-222-2-22-1-2-2-2-2211-1112-1-12-111-111-1-12-2-22-11-11-111-1-111-1000000000000−i3i3−i3i300000000−i3i3−i3i300000000
χ412-2-22-2-2222-2-2222-2-22-222-2-22-1-2-2-2-2211-1112-1-12-111-111-1-12-2-22-11-11-111-1-111-1000000000000i3−i3i3−i300000000i3−i3i3−i300000000
χ422-2-22-2-2222-2-2222-2-22-222-2-2-121111-1-2-22-2-2-122-1-111-111-1-1-111-12-22-2-111-1-111-10000000000000000000000000000−i3i3i3−i3−i3i3i3−i3
χ432-2-22-2-2222-2-2222-2-22-222-2-2-121111-1-2-22-2-2-122-1-111-111-1-1-111-12-22-2-111-1-111-10000000000000000000000000000i3−i3−i3i3i3−i3−i3i3
χ442-2-22-2-2222-2-2222-2-2-22-2-22222-2-2-2-22-2-22-2-222222-2-22-2-222-222-2-22-22-222-2-222-2000000000000000000000000000000000000
χ452-2-22-2-2222-2-2222-2-2-22-2-2222-1-2-2-2-2211-1112-1-12-111-111-1-1-222-21-11-11-1-111-1-11000000000000−i3i3−i3i300000000i3−i3i3−i300000000
χ462-2-22-2-2222-2-2222-2-2-22-2-2222-1-2-2-2-2211-1112-1-12-111-111-1-1-222-21-11-11-1-111-1-11000000000000i3−i3i3−i300000000−i3i3−i3i300000000
χ472-2-22-2-2222-2-2222-2-2-22-2-222-121111-1-2-22-2-2-122-1-111-111-1-11-1-11-22-221-1-111-1-110000000000000000000000000000−i3i3i3−i3i3−i3−i3i3
χ482-2-22-2-2222-2-2222-2-2-22-2-222-121111-1-2-22-2-2-122-1-111-111-1-11-1-11-22-221-1-111-1-110000000000000000000000000000i3−i3−i3i3−i3i3i3−i3
χ492-2-2-222-222-2-22-2-22200000022-2-222-2-2-2222-2-2-222-2-2222-2-200000000000000002-200000000002-2-2200000000000000000000
χ502-2-2-222-222-2-22-2-22200000022-2-222-2-2-2222-2-2-222-2-2222-2-20000000000000000-220000000000-222-200000000000000000000
χ512-2-2-222-222-2-22-2-2220000002-1-2-222-211-1-1-1-2112-111-1-1-11100003−3−333−3−33−333−32-20000000000-111-1000000003−3−3300000000
χ522-2-2-222-222-2-22-2-2220000002-1-2-222-211-1-1-1-2112-111-1-1-11100003−3−333−3−33−333−3-2200000000001-1-1100000000−333−300000000
χ532-2-2-222-222-2-22-2-2220000002-1-2-222-211-1-1-1-2112-111-1-1-1110000−333−3−333−33−3−332-20000000000-111-100000000−333−300000000
χ542-2-2-222-222-2-22-2-2220000002-1-2-222-211-1-1-1-2112-111-1-1-1110000−333−3−333−33−3−33-2200000000001-1-11000000003−3−3300000000
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
χ57444-4-4-4-444444-4-4-4-4000000-24-2-2222444-4-42-4-4-2-2-2-2-222220000000000000000000000000000000000000000000000000000
χ58444-4-4-4-444444-4-4-4-4000000-2-2-2-2222-2-2-222222-21111-1-1-1-100002323−23−23−3−3−3−33333000000000000000000000000000000000000
χ59444-4-4-4-444444-4-4-4-4000000-2-2-2-2222-2-2-222222-21111-1-1-1-10000−23−2323233333−3−3−3−3000000000000000000000000000000000000
χ6044-444-4-4-444-4-4-444-40000004-24-44-4-4-222-224-22-4-2-222-222-20000000000000000000000000000000000000000000000000000
χ6144-444-4-4-444-4-4-444-4000000-2-2-22-222-222-22-2-22211-1-11-1-11−2i3−2i32i32i30000i3i3−i3−i3i3i3−i3−i3000000000000000000000000000000000000
χ6244-444-4-4-444-4-4-444-4000000-2-2-22-222-222-22-2-22211-1-11-1-112i32i3−2i3−2i30000−i3−i3i3i3−i3−i3i3i3000000000000000000000000000000000000
χ6344-4-4-444-444-4-44-4-440000004-24-4-444-2222-2-42-2-4-2-2222-2-220000000000000000000000000000000000000000000000000000
χ6444-4-4-444-444-4-44-4-44000000-24-222-2-24-4-4-442-442-2-2222-2-220000000000000000000000000000000000000000000000000000
χ6544-4-4-444-444-4-44-4-44000000-2-2-222-2-2-2222-222-2211-1-1-111-1000000003i3i−3i−3i−3i−3i3i3i000000000000000000000000000000000000
χ6644-4-4-444-444-4-44-4-44000000-2-2-222-2-2-2222-222-2211-1-1-111-100000000−3i−3i3i3i3i3i−3i−3i000000000000000000000000000000000000
χ674-444-44-4-44-44-4-44-440000004-2-44-44-42-222-24-22-4-22-222-22-20000000000000000000000000000000000000000000000000000
χ684-444-44-4-44-44-4-44-44000000-2-22-22-222-222-2-2-2221-11-1-11-11−2i32i3−2i32i30000i3−i3i3−i3i3−i3i3−i3000000000000000000000000000000000000
χ694-444-44-4-44-44-4-44-44000000-2-22-22-222-222-2-2-2221-11-1-11-112i3−2i32i3−2i30000−i3i3−i3i3−i3i3−i3i3000000000000000000000000000000000000
χ704-44-44-44-44-44-44-44-40000004-2-444-442-22-22-42-2-4-22-22-22-220000000000000000000000000000000000000000000000000000
χ714-44-44-44-44-44-44-44-4000000-242-2-22-2-44-44-42-442-22-22-22-220000000000000000000000000000000000000000000000000000
χ724-44-44-44-44-44-44-44-4000000-2-22-2-22-22-22-2222-221-11-11-11-1000000003i−3i3i−3i−3i3i−3i3i000000000000000000000000000000000000
χ734-44-44-44-44-44-44-44-4000000-2-22-2-22-22-22-2222-221-11-11-11-100000000−3i3i−3i3i3i−3i3i−3i000000000000000000000000000000000000
χ744-4-44-4-4444-4-4444-4-44-444-4-4-2-22222-222-222-2-2-2-21-1-11-1-111-222-2-22-221-1-111-1-11000000000000000000000000000000000000
χ754-4-44-4-4444-4-4444-4-4-44-4-444-2-22222-222-222-2-2-2-21-1-11-1-1112-2-222-22-2-111-1-111-1000000000000000000000000000000000000
χ764-4-4-444-444-4-44-4-444000000-2422-2-22-4-44442-4-4-2-222-2-2-2220000000000000000000000000000000000000000000000000000
χ774-4-4-444-444-4-44-4-444000000-2-222-2-2222-2-2-2222-21-1-1111-1-1000023−23−2323−333−33−3−33000000000000000000000000000000000000
χ784-4-4-444-444-4-44-4-444000000-2-222-2-2222-2-2-2222-21-1-1111-1-10000−232323−233−3−33−333−3000000000000000000000000000000000000
χ7966666666-3-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000000000000222200000000-1-1-1-1-1-1-1-1000000000000
χ8066666666-3-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000000000000-2-2-2-20000000011111111000000000000
χ8166666666-3-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000000000000022-2-200000000-1-1-1-11111000000000000
χ8266666666-3-3-3-3-3-3-3-3-6-6333300000000000000000000000000000000000000000000-2-222000000001111-1-1-1-1000000000000
χ8366-6-6-666-6-3-333-333-30033−3333−33000000000000000000000000000000000000000000002i−2i0000000000−i−iii−i3i3−i3i3000000000000
χ8466-6-6-666-6-3-333-333-30033−3333−3300000000000000000000000000000000000000000000−2i2i0000000000ii−i−ii3−i3i3−i3000000000000
χ8566-6-6-666-6-3-333-333-300−3333−3333000000000000000000000000000000000000000000002i−2i0000000000−i−iiii3−i3i3−i3000000000000
χ8666-6-6-666-6-3-333-333-300−3333−333300000000000000000000000000000000000000000000−2i2i0000000000ii−i−i−i3i3−i3i3000000000000
χ876-66-66-66-6-33-33-33-330033−33−333300000000000000000000000000000000000000000000002i−2i00000000−i3i3−i3i3−i−iii000000000000
χ886-66-66-66-6-33-33-33-330033−33−33330000000000000000000000000000000000000000000000−2i2i00000000i3−i3i3−i3ii−i−i000000000000
χ896-66-66-66-6-33-33-33-3300−333333−3300000000000000000000000000000000000000000000002i−2i00000000i3−i3i3−i3−i−iii000000000000
χ906-66-66-66-6-33-33-33-3300−333333−330000000000000000000000000000000000000000000000−2i2i00000000−i3i3−i3i3ii−i−i000000000000
χ916-6-66-6-666-333-3-3-3336-6-3-333000000000000000000000000000000000000000000000000000000003−3−33−333−3000000000000
χ926-6-66-6-666-333-3-3-3336-6-3-33300000000000000000000000000000000000000000000000000000000−333−33−3−33000000000000
χ936-6-66-6-666-333-3-3-333-6633-3-3000000000000000000000000000000000000000000000000000000003−3−333−3−33000000000000
χ946-6-66-6-666-333-3-3-333-6633-3-300000000000000000000000000000000000000000000000000000000−333−3−333−3000000000000
χ95121212-12-12-12-1212-6-6-6-666660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ961212-121212-12-12-12-6-6666-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-121212-1212-12-12-66-666-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-12-12-121212-1212-666-666-6-60000000000000000000000000000000000000000000000000000000000000000000000000000000000

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