Finite Group Databasebeta

← Group #13140265

Character table — Group #13140265

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222224444446666666666666666121212121212121212121212121212121212121212121212363636363636363636363636363636363636363636363636363636363636363636363636
order1222222236666666441212121233666666666666663666666612121212121212121212121212121212222222444444666666666666121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ71111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ81111111111111111-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ922222222222222222222222-122222-1-1-1-1-12-12-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100002200002200000000-1-1-1-100000000-1-1-1-1
χ1022222222222222222222222-122222-1-1-1-1-12-12-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-2-20000-2-2000000001111000000001111
χ112222222222222222222222-12-1-1-1-1-122222-12-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10022000022000000-1-1-1-100000000-1-1-1-10000
χ122222222222222222222222-12-1-1-1-1-122222-12-12-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100-2-20000-2-200000011110000000011110000
χ132222222222222222-2-2-2-2-2-22-122222-1-1-1-1-12-12-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000220000-2-200000000-1-1-1-1000000001111
χ142222222222222222-2-2-2-2-2-22-122222-1-1-1-1-12-12-1-1-1-1-1-1-1-1-1-2-2-2-21111111111110000-2-200002200000000111100000000-1-1-1-1
χ152222222222222222-2-2-2-2-2-2-12-1-1-1-1-122222-12-12-1-1-1-1-1-1-1-11111-2-2-2-21111111100220000-2-2000000-1-1-1-10000000011110000
χ162222222222222222-2-2-2-2-2-2-12-1-1-1-1-122222-12-12-1-1-1-1-1-1-1-11111-2-2-2-21111111100-2-2000022000000111100000000-1-1-1-10000
χ172222-2-2-2-22222-2-2-2-22i−2i2i2i−2i−2i22222-2-2222-2-2-2-2-2-22222-2-2-2-22i2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ182222-2-2-2-22222-2-2-2-22i−2i2i2i−2i−2i2-1222-2-2-1-1-111-21-21-1-1-1-111112i2i−2i−2i−i−iii−i−i−i−iiiii00000000000000000000−i3−i3i3i30000000033−3−3
χ192222-2-2-2-22222-2-2-2-22i−2i2i2i−2i−2i2-1222-2-2-1-1-111-21-21-1-1-1-111112i2i−2i−2i−i−iii−i−i−i−iiiii00000000000000000000i3i3−i3−i300000000−3−333
χ202222-2-2-2-22222-2-2-2-22i−2i2i2i−2i−2i-12-1-1-111222-2-21-21-2-1-1-1-11111−i−iii2i2i−2i−2i−i−i−i−iiiii0000000000000000−i3−i3i3i30000000033−3−30000
χ212222-2-2-2-22222-2-2-2-22i−2i2i2i−2i−2i-12-1-1-111222-2-21-21-2-1-1-1-11111−i−iii2i2i−2i−2i−i−i−i−iiiii0000000000000000i3i3−i3−i300000000−3−3330000
χ222222-2-2-2-22222-2-2-2-2−2i2i−2i−2i2i2i22222-2-2222-2-2-2-2-2-22222-2-2-2-2−2i−2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ232222-2-2-2-22222-2-2-2-2−2i2i−2i−2i2i2i2-1222-2-2-1-1-111-21-21-1-1-1-11111−2i−2i2i2iii−i−iiiii−i−i−i−i00000000000000000000−i3−i3i3i300000000−3−333
χ242222-2-2-2-22222-2-2-2-2−2i2i−2i−2i2i2i2-1222-2-2-1-1-111-21-21-1-1-1-11111−2i−2i2i2iii−i−iiiii−i−i−i−i00000000000000000000i3i3−i3−i30000000033−3−3
χ252222-2-2-2-22222-2-2-2-2−2i2i−2i−2i2i2i-12-1-1-111222-2-21-21-2-1-1-1-11111ii−i−i−2i−2i2i2iiiii−i−i−i−i0000000000000000−i3−i3i3i300000000−3−3330000
χ262222-2-2-2-22222-2-2-2-2−2i2i−2i−2i2i2i-12-1-1-111222-2-21-21-2-1-1-1-11111ii−i−i−2i−2i2i2iiiii−i−i−i−i0000000000000000i3i3−i3−i30000000033−3−30000
χ2722-2-222-2-222-2-22-22-2000000222-2-22-22-2-2-2-222-2222-2-22-2-22000000000000000000000000002-2000000000000000000002-22-2
χ2822-2-222-2-222-2-22-22-2000000222-2-22-22-2-2-2-222-2222-2-22-2-2200000000000000000000000000-2200000000000000000000-22-22
χ2922-2-222-2-222-2-22-22-20000002-12-2-22-2-111112-1-2-1-1-111-111-10000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i300000000002-200000000−i3i3−i3i300000000-11-11
χ3022-2-222-2-222-2-22-22-20000002-12-2-22-2-111112-1-2-1-1-111-111-10000−i3i3−i3i3−i3−i3i3i3−i3−i3i3i30000000000-2200000000i3−i3i3−i3000000001-11-1
χ3122-2-222-2-222-2-22-22-20000002-12-2-22-2-111112-1-2-1-1-111-111-10000i3−i3i3−i3i3i3−i3−i3i3i3−i3−i300000000002-200000000i3−i3i3−i300000000-11-11
χ3222-2-222-2-222-2-22-22-20000002-12-2-22-2-111112-1-2-1-1-111-111-10000i3−i3i3−i3i3i3−i3−i3i3i3−i3−i30000000000-2200000000−i3i3−i3i3000000001-11-1
χ3322-2-2-2-22222-2-2-22-22000000222-2-2-222-2-222-2-22-222-2-2-222-2000000000000000000002-2000000000000002-2-22000000000000
χ3422-2-2-2-22222-2-2-22-22000000222-2-2-222-2-222-2-22-222-2-2-222-200000000000000000000-2200000000000000-222-2000000000000
χ3522-2-2-2-22222-2-2-22-220000002-12-2-2-22-111-1-1-2121-1-1111-1-1100003−3−3333−3−3−3−33300002-200000000000000-111-1000000003−3−33
χ3622-2-2-2-22222-2-2-22-220000002-12-2-2-22-111-1-1-2121-1-1111-1-1100003−3−3333−3−3−3−3330000-22000000000000001-1-1100000000−333−3
χ3722-2-2-2-22222-2-2-22-220000002-12-2-2-22-111-1-1-2121-1-1111-1-110000−333−3−3−33333−3−300002-200000000000000-111-100000000−333−3
χ3822-2-2-2-22222-2-2-22-220000002-12-2-2-22-111-1-1-2121-1-1111-1-110000−333−3−3−33333−3−30000-22000000000000001-1-11000000003−3−33
χ392-22-22-22-22-22-2-222-200000022-22-2-2-2-22-22-2222-22-22-2-22-220000000000000000000000002-20000000000000000002-22-20000
χ402-22-22-22-22-22-2-222-200000022-22-2-2-2-22-22-2222-22-22-2-22-22000000000000000000000000-22000000000000000000-22-220000
χ412-22-22-22-22-22-2-222-2000000-121-1111-22-22-2-12-1-2-11-111-11-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i3000000002-2000000−i3i3−i3i300000000-11-110000
χ422-22-22-22-22-22-2-222-2000000-121-1111-22-22-2-12-1-2-11-111-11-1−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i300000000-22000000i3−i3i3−i3000000001-11-10000
χ432-22-22-22-22-22-2-222-2000000-121-1111-22-22-2-12-1-2-11-111-11-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i3000000002-2000000i3−i3i3−i300000000-11-110000
χ442-22-22-22-22-22-2-222-2000000-121-1111-22-22-2-12-1-2-11-111-11-1i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i300000000-22000000−i3i3−i3i3000000001-11-10000
χ452-22-2-22-222-22-22-2-2200000022-22-222-22-2-22-2-2-222-22-22-22-20000000000000000002-20000000000002-2-220000000000000000
χ462-22-2-22-222-22-22-2-2200000022-22-222-22-2-22-2-2-222-22-22-22-2000000000000000000-22000000000000-222-20000000000000000
χ472-22-2-22-222-22-22-2-22000000-121-11-1-1-22-2-221-212-11-11-11-113−3−3300003−33−3−33−33002-2000000000000-111-1000000003−3−330000
χ482-22-2-22-222-22-22-2-22000000-121-11-1-1-22-2-221-212-11-11-11-113−3−3300003−33−3−33−3300-220000000000001-1-1100000000−333−30000
χ492-22-2-22-222-22-22-2-22000000-121-11-1-1-22-2-221-212-11-11-11-11−333−30000−33−333−33−3002-2000000000000-111-100000000−333−30000
χ502-22-2-22-222-22-22-2-22000000-121-11-1-1-22-2-221-212-11-11-11-11−333−30000−33−333−33−300-220000000000001-1-11000000003−3−330000
χ512-2-222-2-222-2-22-2-22200000022-2-22-22-2-22-2222-2-22-2-22-2-22200000000000000000000002-2000000000000000022-2-200000000
χ522-2-222-2-222-2-22-2-22200000022-2-22-22-2-22-2222-2-22-2-22-2-2220000000000000000000000-220000000000000000-2-22200000000
χ532-2-22-222-22-2-2222-2-200000022-2-222-2-2-222-2-2-2222-2-2222-2-200000000000000002-2000000000022-2-200000000000000000000
χ542-2-22-222-22-2-2222-2-200000022-2-222-2-2-222-2-2-2222-2-2222-2-20000000000000000-220000000000-2-22200000000000000000000
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
χ574444-4-4-4-44444-4-4-4-44i−4i4i4i−4i−4i-2-2-2-2-222-2-2-22222221111-1-1-1-1−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−i000000000000000000000000000000000000
χ584444-4-4-4-44444-4-4-4-4−4i4i−4i−4i4i4i-2-2-2-2-222-2-2-22222221111-1-1-1-12i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii000000000000000000000000000000000000
χ5944-4-444-4-444-4-44-44-4000000-24-222-224-4-4-4-4-2424-2-222-222-20000000000000000000000000000000000000000000000000000
χ6044-4-444-4-444-4-44-44-4000000-2-2-222-22-22222-2-22-211-1-11-1-110000−2i32i3−2i32i3i3i3−i3−i3i3i3−i3−i3000000000000000000000000000000000000
χ6144-4-444-4-444-4-44-44-4000000-2-2-222-22-22222-2-22-211-1-11-1-1100002i3−2i32i3−2i3−i3−i3i3i3−i3−i3i3i3000000000000000000000000000000000000
χ6244-4-4-4-44444-4-4-44-44000000-24-2222-24-4-4442-4-2-4-2-2222-2-220000000000000000000000000000000000000000000000000000
χ6344-4-4-4-44444-4-4-44-44000000-2-2-2222-2-222-2-222-2211-1-1-111-1000023−23−2323−3−33333−3−3000000000000000000000000000000000000
χ6444-4-4-4-44444-4-4-44-44000000-2-2-2222-2-222-2-222-2211-1-1-111-10000−232323−2333−3−3−3−333000000000000000000000000000000000000
χ654-44-44-44-44-44-4-444-40000004-2-44-4-4-42-22-224-242-22-222-22-20000000000000000000000000000000000000000000000000000
χ664-44-44-44-44-44-4-444-4000000-2-22-22222-22-22-2-2-221-11-1-11-11−2i32i3−2i32i30000i3−i3i3−i3i3−i3i3−i3000000000000000000000000000000000000
χ674-44-44-44-44-44-4-444-4000000-2-22-22222-22-22-2-2-221-11-1-11-112i3−2i32i3−2i30000−i3i3−i3i3−i3i3−i3i3000000000000000000000000000000000000
χ684-44-4-44-444-44-44-4-440000004-2-44-4442-222-2-42-4-2-22-22-22-220000000000000000000000000000000000000000000000000000
χ694-44-4-44-444-44-44-4-44000000-2-22-22-2-22-222-2222-21-11-11-11-123−23−23230000−33−333−33−3000000000000000000000000000000000000
χ704-44-4-44-444-44-44-4-44000000-2-22-22-2-22-222-2222-21-11-11-11-1−232323−2300003−33−3−33−33000000000000000000000000000000000000
χ714-4-444-4-444-4-44-4-4440000004-2-4-44-4422-22-24-2-42-222-222-2-20000000000000000000000000000000000000000000000000000
χ724-4-444-4-444-4-44-4-444000000-2422-22-2-4-44-44-242-4-222-222-2-20000000000000000000000000000000000000000000000000000
χ734-4-444-4-444-4-44-4-444000000-2-222-22-222-22-2-2-2221-1-11-1-111000000003-3-333-3-33000000000000000000000000000000000000
χ744-4-444-4-444-4-44-4-444000000-2-222-22-222-22-2-2-2221-1-11-1-11100000000-333-3-333-3000000000000000000000000000000000000
χ754-4-44-444-44-4-4444-4-40000004-2-4-444-422-2-22-424-2-222-2-2-2220000000000000000000000000000000000000000000000000000
χ764-4-44-444-44-4-4444-4-4000000-2422-2-22-4-444-42-4-24-222-2-2-2220000000000000000000000000000000000000000000000000000
χ774-4-44-444-44-4-4444-4-4000000-2-222-2-2222-2-2222-2-21-1-1111-1-1000000003i−3i−3i3i−3i3i3i−3i000000000000000000000000000000000000
χ784-4-44-444-44-4-4444-4-4000000-2-222-2-2222-2-2222-2-21-1-1111-1-100000000−3i3i3i−3i3i−3i−3i3i000000000000000000000000000000000000
χ7966666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000220000220000-1-1-1-100000000-1-1-1-100000000
χ8066666666-3-3-3-3-3-3-3-366-3-3-3-30000000000000000000000000000000000000000-2-20000-2-20000111100000000111100000000
χ8166666666-3-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000000000220000-2-20000-1-1-1-100000000111100000000
χ8266666666-3-3-3-3-3-3-3-3-6-633330000000000000000000000000000000000000000-2-20000220000111100000000-1-1-1-100000000
χ836666-6-6-6-6-3-3-3-333336i−6i−3i−3i3i3i0000000000000000000000000000000000000000000000000000−i3i3−i3i3000000003−33−300000000
χ846666-6-6-6-6-3-3-3-333336i−6i−3i−3i3i3i0000000000000000000000000000000000000000000000000000i3−i3i3−i300000000−33−3300000000
χ856666-6-6-6-6-3-3-3-33333−6i6i3i3i−3i−3i0000000000000000000000000000000000000000000000000000−i3i3−i3i300000000−33−3300000000
χ866666-6-6-6-6-3-3-3-33333−6i6i3i3i−3i−3i0000000000000000000000000000000000000000000000000000i3−i3i3−i3000000003−33−300000000
χ876-6-666-6-66-333-333-3-300−3i33i3−3i33i300000000000000000000000000000000000000000000002-20000−i3i3i3−i300000000-1-11100000000
χ886-6-666-6-66-333-333-3-300−3i33i3−3i33i30000000000000000000000000000000000000000000000-220000i3−i3−i3i30000000011-1-100000000
χ896-6-666-6-66-333-333-3-3003i3−3i33i3−3i300000000000000000000000000000000000000000000002-20000i3−i3−i3i300000000-1-11100000000
χ906-6-666-6-66-333-333-3-3003i3−3i33i3−3i30000000000000000000000000000000000000000000000-220000−i3i3i3−i30000000011-1-100000000
χ916-6-66-666-6-333-3-3-3330033−33−333300000000000000000000000000000000000000002-20000000000-1-111000000003−3−3300000000
χ926-6-66-666-6-333-3-3-3330033−33−33330000000000000000000000000000000000000000-22000000000011-1-100000000−333−300000000
χ936-6-66-666-6-333-3-3-33300−333333−3300000000000000000000000000000000000000002-20000000000-1-11100000000−333−300000000
χ946-6-66-666-6-333-3-3-33300−333333−330000000000000000000000000000000000000000-22000000000011-1-1000000003−3−3300000000
χ951212-12-121212-12-12-6-666-66-660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ961212-12-12-12-121212-6-6666-66-60000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9712-1212-1212-1212-12-66-666-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9812-1212-12-1212-1212-66-66-666-60000000000000000000000000000000000000000000000000000000000000000000000000000000000

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