Finite Group Databasebeta

← Group #13149560

Character table — Group #13149560

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size111122222222224444446666666612121212121212121212121212121212181818181818181818181818181818181818242424242424363636363636363636363636363636363636363636363636363636
order1222344444466612121212121233666666366612121212121212121212121222444466661212121212121212121212121212222444444666666121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-11-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ311111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111111-1-1-111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-111-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-1-1-1
χ51111111-1-1-1-1111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11-1-11-1-11-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111-1-1-1-1111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-111111-1-1-1-1-111111111-1-111-1-1-1-1
χ71111111-1-1-1-1111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111-1-1-1-1111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111111-1-11111
χ911111-1-111-1-111111-1-1-1-1111111111111-1-1-1-111-1-111-1-1111111111111111111-1-111-1-1-11-1-11-1-11-1-1-111-1-111-1-1-1-1-1-111-1-1
χ1011111-1-111-1-111111-1-1-1-1111111111111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11-11-1-1111-111-1-111-1-11111-1-111-1-1
χ1111111-1-111-1-111111-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1111-11-11-1-1-1-11111-1-11111-1-111
χ1211111-1-111-1-111111-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-11-11-1-111111-1-1-1-111-1-111-1-111
χ1311111-1-1-1-111111-1-111-1-1111111111111-1-1-1-1-1-111-1-111111111111111111111-1-1-1-111-1-11-1-11-1-11-1-1-1-111-1-111-1-1-1-1-1-111
χ1411111-1-1-1-111111-1-111-1-1111111111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-11-111111-1-111-1-111-1-1-1-111
χ1511111-1-1-1-111111-1-111-1-1111111111111-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-11-11-1111-1-1-111-1-1-1-111111111-1-1
χ1611111-1-1-1-111111-1-111-1-1111111111111-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111-1111-1-11-111-1-11111-1-1-1-11111-1-1
χ17222222222222222222222-12-1-12-12-1-1-1-1-1-122-1-1-1-1222200002200000000-1-1-1-1-1-1-1-1-1-102200020000-1-1-1-10000-1-1000000
χ18222222222222222222222-12-1-12-12-1-1-1-1-1-122-1-1-1-122220000-2-2000000001111-1-1-1-1-1-10-2-2000-200001111000011000000
χ1922222222222222222222-12-122-12-1-1-1-1-122-1-12222-1-1-1-1220000-1-1-1-100000000-1-1-1-1-1-1000200022000000000000-1-1-1-1-1-1
χ2022222222222222222222-12-122-12-1-1-1-1-122-1-12222-1-1-1-1-2-20000111100000000-1-1-1-1-1-1000-2000-2-2000000000000111111
χ212222222-2-2-2-2222-2-2-2-2222-12-1-12-12-1-1-1-1-1-1221111-2-2-2-200002200000000-1-1-1-1-1-111110-2-20002000011110000-1-1000000
χ222222222-2-2-2-2222-2-2-2-2222-12-1-12-12-1-1-1-1-1-1221111-2-2-2-20000-2-2000000001111-1-11111022000-20000-1-1-1-1000011000000
χ232222222-2-2-2-2222-2-2-2-222-12-122-12-1-1-1-1-122-1-1-2-2-2-21111220000-1-1-1-100000000-1-111110002000-2-2000000000000-1-11111
χ242222222-2-2-2-2222-2-2-2-222-12-122-12-1-1-1-1-122-1-1-2-2-2-21111-2-20000111100000000-1-11111000-20002200000000000011-1-1-1-1
χ2522222-2-222-2-222222-2-2-2-22-12-1-12-12-1-1-1-111-2-2-1-11122-2-200002200000000-1-1-1-111-1-11102-2000-20000-1-111000011000000
χ2622222-2-222-2-222222-2-2-2-22-12-1-12-12-1-1-1-111-2-2-1-11122-2-20000-2-200000000111111-1-1110-220002000011-1-10000-1-1000000
χ2722222-2-222-2-222222-2-2-2-2-12-122-12-1-1-1-1-1-2-21122-2-2-1-111220000-1-1-1-10000000011-1-111000-20002-200000000000011-1-111
χ2822222-2-222-2-222222-2-2-2-2-12-122-12-1-1-1-1-1-2-21122-2-2-1-111-2-2000011110000000011-1-1110002000-22000000000000-1-111-1-1
χ2922222-2-2-2-222222-2-222-2-22-12-1-12-12-1-1-1-111-2-211-1-1-2-22200002200000000-1-1-1-11111-1-10-22000-2000011-1-1000011000000
χ3022222-2-2-2-222222-2-222-2-22-12-1-12-12-1-1-1-111-2-211-1-1-2-2220000-2-20000000011111111-1-102-200020000-1-1110000-1-1000000
χ3122222-2-2-2-222222-2-222-2-2-12-122-12-1-1-1-1-1-2-211-2-22211-1-1220000-1-1-1-1000000001111-1-1000-2000-220000000000001111-1-1
χ3222222-2-2-2-222222-2-222-2-2-12-122-12-1-1-1-1-1-2-211-2-22211-1-1-2-200001111000000001111-1-100020002-2000000000000-1-1-1-111
χ3322-2-222-22i−2i2i−2i-22-22i−2i2i−2i2-222-22-22-2-22-22-22-22-22i−2i2i−2i2i−2i2i−2i0000000000000000002-22i−2i2i−2i000000000000000000000000000
χ3422-2-222-22i−2i2i−2i-22-22i−2i2i−2i2-22-1-2-1121-2-11-11-112-2−ii−ii2i−2i2i−2i0000000000000033−3−3-11−ii−ii00000000000−i3i3−i3i300003−3000000
χ3522-2-222-22i−2i2i−2i-22-22i−2i2i−2i2-22-1-2-1121-2-11-11-112-2−ii−ii2i−2i2i−2i00000000000000−3−333-11−ii−ii00000000000i3−i3i3−i30000−33000000
χ3622-2-222-22i−2i2i−2i-22-22i−2i2i−2i2-2-1212-2-1-21-11-112-2-112i−2i2i−2i−ii−ii000000−i3−i3i3i300000000-11−ii−ii000000000000000000000−i3i33−33−3
χ3722-2-222-22i−2i2i−2i-22-22i−2i2i−2i2-2-1212-2-1-21-11-112-2-112i−2i2i−2i−ii−ii000000i3i3−i3−i300000000-11−ii−ii000000000000000000000i3−i3−33−33
χ3822-2-222-2−2i2i−2i2i-22-2−2i2i−2i2i2-222-22-22-2-22-22-22-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000002-2−2i2i−2i2i000000000000000000000000000
χ3922-2-222-2−2i2i−2i2i-22-2−2i2i−2i2i2-22-1-2-1121-2-11-11-112-2i−ii−i−2i2i−2i2i0000000000000033−3−3-11i−ii−i00000000000i3−i3i3−i300003−3000000
χ4022-2-222-2−2i2i−2i2i-22-2−2i2i−2i2i2-22-1-2-1121-2-11-11-112-2i−ii−i−2i2i−2i2i00000000000000−3−333-11i−ii−i00000000000−i3i3−i3i30000−33000000
χ4122-2-222-2−2i2i−2i2i-22-2−2i2i−2i2i2-2-1212-2-1-21-11-112-2-11−2i2i−2i2ii−ii−i000000−i3−i3i3i300000000-11i−ii−i000000000000000000000−i3i3−33−33
χ4222-2-222-2−2i2i−2i2i-22-2−2i2i−2i2i2-2-1212-2-1-21-11-112-2-11−2i2i−2i2ii−ii−i000000i3i3−i3−i300000000-11i−ii−i000000000000000000000i3−i33−33−3
χ4322-2-22-222i−2i−2i2i-22-22i−2i−2i2i-2222-22-22-2-22-22-2-22-222i−2i−2i2i2i−2i−2i2i000000000000000000-222i−2i−2i2i000000000000000000000000000
χ4422-2-22-222i−2i−2i2i-22-22i−2i−2i2i-222-1-2-1121-2-11-111-1-22−iii−i2i−2i−2i2i0000000000000033−3−31-1−iii−i00000000000−i3i3i3−i30000−33000000
χ4522-2-22-222i−2i−2i2i-22-22i−2i−2i2i-222-1-2-1121-2-11-111-1-22−iii−i2i−2i−2i2i00000000000000−3−3331-1−iii−i00000000000i3−i3−i3i300003−3000000
χ4622-2-22-222i−2i−2i2i-22-22i−2i−2i2i-22-1212-2-1-21-11-11-221-12i−2i−2i2i−iii−i000000−i3−i3i3i3000000001-1−iii−i000000000000000000000i3−i33−3−33
χ4722-2-22-222i−2i−2i2i-22-22i−2i−2i2i-22-1212-2-1-21-11-11-221-12i−2i−2i2i−iii−i000000i3i3−i3−i3000000001-1−iii−i000000000000000000000−i3i3−333−3
χ4822-2-22-22−2i2i2i−2i-22-2−2i2i2i−2i-2222-22-22-2-22-22-2-22-22−2i2i2i−2i−2i2i2i−2i000000000000000000-22−2i2i2i−2i000000000000000000000000000
χ4922-2-22-22−2i2i2i−2i-22-2−2i2i2i−2i-222-1-2-1121-2-11-111-1-22i−i−ii−2i2i2i−2i0000000000000033−3−31-1i−i−ii00000000000i3−i3−i3i30000−33000000
χ5022-2-22-22−2i2i2i−2i-22-2−2i2i2i−2i-222-1-2-1121-2-11-111-1-22i−i−ii−2i2i2i−2i00000000000000−3−3331-1i−i−ii00000000000−i3i3i3−i300003−3000000
χ5122-2-22-22−2i2i2i−2i-22-2−2i2i2i−2i-22-1212-2-1-21-11-11-221-1−2i2i2i−2ii−i−ii000000−i3−i3i3i3000000001-1i−i−ii000000000000000000000i3−i3−333−3
χ5222-2-22-22−2i2i2i−2i-22-2−2i2i2i−2i-22-1212-2-1-21-11-11-221-1−2i2i2i−2ii−i−ii000000i3i3−i3−i3000000001-1i−i−ii000000000000000000000−i3i33−3−33
χ532-22-22000000-2-22000000222-22-2-2-222-2-20000000000002-22i−2i2i−2i2-22-22i2i−2i−2i2i−2i2i−2i000000000000000000000000000000000
χ542-22-22000000-2-22000000222-22-2-2-222-2-20000000000002-2−2i2i−2i2i2-22-2−2i−2i2i2i−2i2i−2i2i000000000000000000000000000000000
χ552-22-22000000-2-22000000222-22-2-2-222-2-2000000000000-222i−2i−2i2i-22-222i2i−2i−2i−2i2i−2i2i000000000000000000000000000000000
χ562-22-22000000-2-22000000222-22-2-2-222-2-2000000000000-22−2i2i2i−2i-22-22−2i−2i2i2i2i−2i2i−2i000000000000000000000000000000000
χ5744444444444444444444-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000111111000000000000000000000000000
χ584444444-4-4-4-4444-4-4-4-444-2-2-2-2-2-2-2-21111-2-2-2-22222222200000000000000000011-1-1-1-1000000000000000000000000000
χ5944444-4-444-4-444444-4-4-4-4-2-2-2-2-2-2-2-211112222-2-222-2-222000000000000000000-1-111-1-1000000000000000000000000000
χ6044444-4-4-4-444444-4-444-4-4-2-2-2-2-2-2-2-21111222222-2-222-2-2000000000000000000-1-1-1-111000000000000000000000000000
χ6144-4-444-44i−4i4i−4i-44-44i−4i4i−4i4-4-2-22-22-2221-11-1-22-22−2i2i−2i2i−2i2i−2i2i0000000000000000001-1i−ii−i000000000000000000000000000
χ6244-4-444-4−4i4i−4i4i-44-4−4i4i−4i4i4-4-2-22-22-2221-11-1-22-222i−2i2i−2i2i−2i2i−2i0000000000000000001-1−ii−ii000000000000000000000000000
χ6344-4-44-444i−4i−4i4i-44-44i−4i−4i4i-44-2-22-22-2221-11-12-22-2−2i2i2i−2i−2i2i2i−2i000000000000000000-11i−i−ii000000000000000000000000000
χ6444-4-44-44−4i4i4i−4i-44-4−4i4i4i−4i-44-2-22-22-2221-11-12-22-22i−2i−2i2i2i−2i−2i2i000000000000000000-11−iii−i000000000000000000000000000
χ654-44-44000000-4-440000004-242-2-42-4-2-22200000000000000004i−4i00000000−2i2i−2i2i000000000000000000000000000000000
χ664-44-44000000-4-440000004-242-2-42-4-2-2220000000000000000−4i4i000000002i−2i2i−2i000000000000000000000000000000000
χ674-44-44000000-4-44000000-24-2-442-42-2-2220000000000004-40000-22-2200000000000000000000000000000000000000000
χ684-44-44000000-4-44000000-24-2-442-42-2-222000000000000-4400002-22-200000000000000000000000000000000000000000
χ694-4-4440000004-4-400000044-4-4-4-4444-4-44000000000000000000000000000000000000000000000000000000000000000
χ704-4-4440000004-4-40000004-2-422-4-24-222-200000000000000000000000000−2i32i32i3−2i3000000000000000000000000000000000
χ714-4-4440000004-4-40000004-2-422-4-24-222-2000000000000000000000000002i3−2i3−2i32i3000000000000000000000000000000000
χ724-4-4440000004-4-4000000-242-4-424-2-222-2000000000000000000−2i32i32i3−2i300000000000000000000000000000000000000000
χ734-4-4440000004-4-4000000-242-4-424-2-222-20000000000000000002i3−2i3−2i32i300000000000000000000000000000000000000000
χ746666-3666666-3-3-3-3-3-3-3-3-30000000000000000000000000022000000-1-1-1-10000000000200022000-1-10000-1-1-1-100000000
χ756666-3666666-3-3-3-3-3-3-3-3-300000000000000000000000000-2-200000011110000000000-2000-2-2000110000111100000000
χ766666-366-6-6-6-6-3-3-33333-3-30000000000000000000000000022000000-1-1-1-100000000002000-2-2000-1-10000111100000000
χ776666-366-6-6-6-6-3-3-33333-3-300000000000000000000000000-2-200000011110000000000-200022000110000-1-1-1-100000000
χ786666-3-6-666-6-6-3-3-3-3-333330000000000000000000000000022000000-1-1-1-10000000000-20002-2000110000-1-11100000000
χ796666-3-6-666-6-6-3-3-3-3-3333300000000000000000000000000-2-2000000111100000000002000-22000-1-1000011-1-100000000
χ806666-3-6-6-6-666-3-3-333-3-3330000000000000000000000000022000000-1-1-1-10000000000-2000-2200011000011-1-100000000
χ816666-3-6-6-6-666-3-3-333-3-33300000000000000000000000000-2-20000001111000000000020002-2000-1-10000-1-11100000000
χ8266-6-6-36-66i−6i6i−6i3-33−3i3i−3i3i-330000000000000000000000000000000000−i3i3−i3i30000000000000000000−i3i300003−33−300000000
χ8366-6-6-36-66i−6i6i−6i3-33−3i3i−3i3i-330000000000000000000000000000000000i3−i3i3−i30000000000000000000i3−i30000−33−3300000000
χ8466-6-6-36-6−6i6i−6i6i3-333i−3i3i−3i-330000000000000000000000000000000000−i3i3−i3i30000000000000000000−i3i30000−33−3300000000
χ8566-6-6-36-6−6i6i−6i6i3-333i−3i3i−3i-330000000000000000000000000000000000i3−i3i3−i30000000000000000000i3−i300003−33−300000000
χ8666-6-6-3-666i−6i−6i6i3-33−3i3i3i−3i3-30000000000000000000000000000000000−i3i3−i3i30000000000000000000i3−i300003−3−3300000000
χ8766-6-6-3-666i−6i−6i6i3-33−3i3i3i−3i3-30000000000000000000000000000000000i3−i3i3−i30000000000000000000−i3i30000−333−300000000
χ8866-6-6-3-66−6i6i6i−6i3-333i−3i−3i3i3-30000000000000000000000000000000000−i3i3−i3i30000000000000000000i3−i30000−333−300000000
χ8966-6-6-3-66−6i6i6i−6i3-333i−3i−3i3i3-30000000000000000000000000000000000i3−i3i3−i30000000000000000000−i3i300003−3−3300000000
χ908-88-88000000-8-88000000-4-4-44-444422-2-2000000000000000000000000000000000000000000000000000000000000000
χ918-8-8880000008-8-8000000-4-44444-4-42-2-22000000000000000000000000000000000000000000000000000000000000000
χ9212-1212-12-600000066-6000000000000000000000000000000004i−4i000000−2i−2i2i2i0000000000000000000000000000000000000
χ9312-1212-12-600000066-600000000000000000000000000000000−4i4i0000002i2i−2i−2i0000000000000000000000000000000000000
χ9412-12-1212-6000000-666000000000000000000000000000000000000000023−23−23230000000000000000000000000000000000000
χ9512-12-1212-6000000-6660000000000000000000000000000000000000000−232323−230000000000000000000000000000000000000

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