Finite Group Databasebeta

← Group #13149563

Character table — Group #13149563

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size111122222222224444446666666612121212121212121212121212121212181818181818181818181818181818181818242424242424363636363636363636363636363636363636363636363636363636
order122234444446661212121212123366666636661212121212121212121212124444441212121212121212121212121212121212122222444446666666612121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11-1-1-1-1-1-1-1-1111111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-111-1-1
χ411111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ51111111-1-1-1-1111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-11111
χ61111111-1-1-1-1111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111111-1-1-1-1-1-1-1-1
χ71111111-1-1-1-1111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111-1-1-1-1-1-11111-1-1111111-1-1
χ81111111-1-1-1-1111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-11-11111-1-1-1-1-1-11111-1-111
χ911111-1-111-1-111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1111111111111111111-1-111-1-11-11-11-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1
χ1011111-1-111-1-111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-11-111-111-1-1-111-1-111-1-111-1-11111
χ1111111-1-111-1-111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11-1-11-11-11111-1-1-1-11111-1-111-1-111
χ1211111-1-111-1-111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-111-1-111-11-1-11111-1-111-1-11111-1-1
χ1311111-1-1-1-111111-1-111-1-1111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-111-11-11-11-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1
χ1411111-1-1-1-111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1111-111-1-111-1-1-1-1-1-1111111
χ1511111-1-1-1-111111-1-111-1-1111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-111-11-1-111-1-11111-1-11111-1-1-1-111
χ1611111-1-1-1-111111-1-111-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-111-11-1111-1-1-1-1111111-1-111-1-1
χ17222222222222222222222-12-12-12-1-1-1-1-122-1-122-1-122-1-100002200000000-1-1-1-1-1-1-1-1-1-10022000200000-1-1-1-100000000-1-1
χ18222222222222222222222-12-12-12-1-1-1-1-122-1-122-1-122-1-10000-2-2000000001111-1-1-1-1-1-100-2-2000-20000011110000000011
χ1922222222222222222222-12-12-12-12-1-1-1-1-1-122-1-122-1-1220022000000-1-1-1-10000-1-1-1-1-1-1220000200-1-1-1-10000000000-1-100
χ2022222222222222222222-12-12-12-12-1-1-1-1-1-122-1-122-1-12200-2-200000011110000-1-1-1-1-1-1-2-20000-200111100000000001100
χ212222222-2-2-2-2222-2-2-2-2222-12-12-12-1-1-1-1-122-1-1-2-211-2-21100002200000000-1-1-1-1-1-1111100-2-2000200000111100000000-1-1
χ222222222-2-2-2-2222-2-2-2-2222-12-12-12-1-1-1-1-122-1-1-2-211-2-2110000-2-2000000001111-1-111110022000-200000-1-1-1-10000000011
χ232222222-2-2-2-2222-2-2-2-222-12-12-12-12-1-1-1-1-1-12211-2-211-2-20022000000-1-1-1-10000-1-11111-2-2000020011110000000000-1-100
χ242222222-2-2-2-2222-2-2-2-222-12-12-12-12-1-1-1-1-1-12211-2-211-2-200-2-200000011110000-1-11111220000-200-1-1-1-100000000001100
χ2522222-2-222-2-222222-2-2-2-22-12-12-12-1-1-1-1-1-2-21122-1-1-2-21100002200000000-1-1-1-111-1-111002-2000-200000-1-1110000000011
χ2622222-2-222-2-222222-2-2-2-22-12-12-12-1-1-1-1-1-2-21122-1-1-2-2110000-2-200000000111111-1-11100-2200020000011-1-100000000-1-1
χ2722222-2-222-2-222222-2-2-2-2-12-12-12-12-1-1-1-111-2-2-1-12211-2-20022000000-1-1-1-1000011-1-1112-20000-200-1-11100000000001100
χ2822222-2-222-2-222222-2-2-2-2-12-12-12-12-1-1-1-111-2-2-1-12211-2-200-2-20000001111000011-1-111-22000020011-1-10000000000-1-100
χ2922222-2-2-2-222222-2-222-2-22-12-12-12-1-1-1-1-1-2-211-2-21122-1-100002200000000-1-1-1-11111-1-100-22000-20000011-1-10000000011
χ3022222-2-2-2-222222-2-222-2-22-12-12-12-1-1-1-1-1-2-211-2-21122-1-10000-2-20000000011111111-1-1002-2000200000-1-11100000000-1-1
χ3122222-2-2-2-222222-2-222-2-2-12-12-12-12-1-1-1-111-2-211-2-2-1-1220022000000-1-1-1-100001111-1-1-220000-20011-1-100000000001100
χ3222222-2-2-2-222222-2-222-2-2-12-12-12-12-1-1-1-111-2-211-2-2-1-12200-2-2000000111100001111-1-12-20000200-1-1110000000000-1-100
χ3322-2-222-22i−2i2i−2i-2-222i−2i2i−2i2-22222-2-2-2-22-22-22-22-22i−2i2i−2i2i−2i2i−2i0000000000000000002-22i−2i2i−2i000000000000000000000000000
χ3422-2-222-22i−2i2i−2i-2-222i−2i2i−2i2-22-12-1-21-21-11-112-2-112i−2i−ii2i−2i−ii0000000000000033−3−3-11−ii−ii0000000000000−i3i3−i3i3000000003−3
χ3522-2-222-22i−2i2i−2i-2-222i−2i2i−2i2-22-12-1-21-21-11-112-2-112i−2i−ii2i−2i−ii00000000000000−3−333-11−ii−ii0000000000000i3−i3i3−i300000000−33
χ3622-2-222-22i−2i2i−2i-2-222i−2i2i−2i2-2-12-121-21-2-11-11-112-2−ii2i−2i−ii2i−2i000000000033−3−30000-11−ii−ii000000000−i3i3−i3i300000000003−300
χ3722-2-222-22i−2i2i−2i-2-222i−2i2i−2i2-2-12-121-21-2-11-11-112-2−ii2i−2i−ii2i−2i0000000000−3−3330000-11−ii−ii000000000i3−i3i3−i30000000000−3300
χ3822-2-222-2−2i2i−2i2i-2-22−2i2i−2i2i2-22222-2-2-2-22-22-22-22-2−2i2i−2i2i−2i2i−2i2i0000000000000000002-2−2i2i−2i2i000000000000000000000000000
χ3922-2-222-2−2i2i−2i2i-2-22−2i2i−2i2i2-22-12-1-21-21-11-112-2-11−2i2ii−i−2i2ii−i0000000000000033−3−3-11i−ii−i0000000000000i3−i3i3−i3000000003−3
χ4022-2-222-2−2i2i−2i2i-2-22−2i2i−2i2i2-22-12-1-21-21-11-112-2-11−2i2ii−i−2i2ii−i00000000000000−3−333-11i−ii−i0000000000000−i3i3−i3i300000000−33
χ4122-2-222-2−2i2i−2i2i-2-22−2i2i−2i2i2-2-12-121-21-2-11-11-112-2i−i−2i2ii−i−2i2i000000000033−3−30000-11i−ii−i000000000i3−i3i3−i300000000003−300
χ4222-2-222-2−2i2i−2i2i-2-22−2i2i−2i2i2-2-12-121-21-2-11-11-112-2i−i−2i2ii−i−2i2i0000000000−3−3330000-11i−ii−i000000000−i3i3−i3i30000000000−3300
χ4322-2-22-222i−2i−2i2i-2-222i−2i−2i2i-222222-2-2-2-22-22-2-22-222i−2i2i−2i−2i2i−2i2i000000000000000000-222i−2i−2i2i000000000000000000000000000
χ4422-2-22-222i−2i−2i2i-2-222i−2i−2i2i-222-12-1-21-21-11-11-221-12i−2i−ii−2i2ii−i0000000000000033−3−31-1−iii−i0000000000000−i3i3i3−i300000000−33
χ4522-2-22-222i−2i−2i2i-2-222i−2i−2i2i-222-12-1-21-21-11-11-221-12i−2i−ii−2i2ii−i00000000000000−3−3331-1−iii−i0000000000000i3−i3−i3i3000000003−3
χ4622-2-22-222i−2i−2i2i-2-222i−2i−2i2i-22-12-121-21-2-11-111-1-22−ii2i−2ii−i−2i2i000000000033−3−300001-1−iii−i000000000−i3i3i3−i30000000000−3300
χ4722-2-22-222i−2i−2i2i-2-222i−2i−2i2i-22-12-121-21-2-11-111-1-22−ii2i−2ii−i−2i2i0000000000−3−33300001-1−iii−i000000000i3−i3−i3i300000000003−300
χ4822-2-22-22−2i2i2i−2i-2-22−2i2i2i−2i-222222-2-2-2-22-22-2-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000-22−2i2i2i−2i000000000000000000000000000
χ4922-2-22-22−2i2i2i−2i-2-22−2i2i2i−2i-222-12-1-21-21-11-11-221-1−2i2ii−i2i−2i−ii0000000000000033−3−31-1i−i−ii0000000000000i3−i3−i3i300000000−33
χ5022-2-22-22−2i2i2i−2i-2-22−2i2i2i−2i-222-12-1-21-21-11-11-221-1−2i2ii−i2i−2i−ii00000000000000−3−3331-1i−i−ii0000000000000−i3i3i3−i3000000003−3
χ5122-2-22-22−2i2i2i−2i-2-22−2i2i2i−2i-22-12-121-21-2-11-111-1-22i−i−2i2i−ii2i−2i000000000033−3−300001-1i−i−ii000000000i3−i3−i3i30000000000−3300
χ5222-2-22-22−2i2i2i−2i-2-22−2i2i2i−2i-22-12-121-21-2-11-111-1-22i−i−2i2i−ii2i−2i0000000000−3−33300001-1i−i−ii000000000−i3i3i3−i300000000003−300
χ532-22-220000002-2-200000022-2-222-2-222-2-20000000000002-22i−2i2i−2i22-2-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000
χ542-22-220000002-2-200000022-2-222-2-222-2-20000000000002-2−2i2i−2i2i22-2-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000
χ552-22-220000002-2-200000022-2-222-2-222-2-2000000000000-222i−2i−2i2i-2-2222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000
χ562-22-220000002-2-200000022-2-222-2-222-2-2000000000000-22−2i2i2i−2i-2-222−2i2i−2i2i2i−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
χ5944444-4-444-4-444444-4-4-4-4-2-2-2-2-2-2-2-211112222-2-2-2-22222000000000000000000-1-111-1-1000000000000000000000000000
χ6044444-4-4-4-444444-4-444-4-4-2-2-2-2-2-2-2-2111122222222-2-2-2-2000000000000000000-1-1-1-111000000000000000000000000000
χ6144-4-444-44i−4i4i−4i-4-444i−4i4i−4i4-4-2-2-2-222221-11-1-22-22−2i2i−2i2i−2i2i−2i2i0000000000000000001-1i−ii−i000000000000000000000000000
χ6244-4-444-4−4i4i−4i4i-4-44−4i4i−4i4i4-4-2-2-2-222221-11-1-22-222i−2i2i−2i2i−2i2i−2i0000000000000000001-1−ii−ii000000000000000000000000000
χ6344-4-44-444i−4i−4i4i-4-444i−4i−4i4i-44-2-2-2-222221-11-12-22-2−2i2i−2i2i2i−2i2i−2i000000000000000000-11i−i−ii000000000000000000000000000
χ6444-4-44-44−4i4i4i−4i-4-44−4i4i4i−4i-44-2-2-2-222221-11-12-22-22i−2i2i−2i−2i2i−2i2i000000000000000000-11−iii−i000000000000000000000000000
χ654-44-440000004-4-40000004-2-424-2-42-2-22200000000000000004i−4i00000000−2i2i−2i2i000000000000000000000000000000000
χ664-44-440000004-4-40000004-2-424-2-42-2-2220000000000000000−4i4i000000002i−2i2i−2i000000000000000000000000000000000
χ674-44-440000004-4-4000000-242-4-242-4-2-222000000000000004i−4i000000−2i2i−2i2i0000000000000000000000000000000000000
χ684-44-440000004-4-4000000-242-4-242-4-2-22200000000000000−4i4i0000002i−2i2i−2i0000000000000000000000000000000000000
χ694-4-444000000-44-400000044-4-4-4-4444-4-44000000000000000000000000000000000000000000000000000000000000000
χ704-4-444000000-44-40000004-2-42-424-2-222-200000000000000000000000000−2i32i32i3−2i3000000000000000000000000000000000
χ714-4-444000000-44-40000004-2-42-424-2-222-2000000000000000000000000002i3−2i3−2i32i3000000000000000000000000000000000
χ724-4-444000000-44-4000000-242-42-4-24-222-20000000000000000000000−2i32i32i3−2i30000000000000000000000000000000000000
χ734-4-444000000-44-4000000-242-42-4-24-222-200000000000000000000002i3−2i3−2i32i30000000000000000000000000000000000000
χ746666-3666666-3-3-3-3-3-3-3-3-3000000000000000000000000220000-1-1-1-10000000000000000002200200000000-1-1-1-1-1-10000
χ756666-3666666-3-3-3-3-3-3-3-3-3000000000000000000000000-2-200001111000000000000000000-2-200-2000000001111110000
χ766666-366-6-6-6-6-3-3-33333-3-3000000000000000000000000220000-1-1-1-1000000000000000000-2-200200000000-1-111110000
χ776666-366-6-6-6-6-3-3-33333-3-3000000000000000000000000-2-2000011110000000000000000002200-20000000011-1-1-1-10000
χ786666-3-6-666-6-6-3-3-3-3-33333000000000000000000000000220000-1-1-1-10000000000000000002-200-20000000011-1-1110000
χ796666-3-6-666-6-6-3-3-3-3-33333000000000000000000000000-2-200001111000000000000000000-2200200000000-1-111-1-10000
χ806666-3-6-6-6-666-3-3-333-3-333000000000000000000000000220000-1-1-1-1000000000000000000-2200-2000000001111-1-10000
χ816666-3-6-6-6-666-3-3-333-3-333000000000000000000000000-2-2000011110000000000000000002-200200000000-1-1-1-1110000
χ8266-6-6-36-66i−6i6i−6i33-3−3i3i−3i3i-330000000000000000000000000000003−33−300000000000000000000000000000003−3−i3i3−i3i30000
χ8366-6-6-36-66i−6i6i−6i33-3−3i3i−3i3i-33000000000000000000000000000000−33−330000000000000000000000000000000−33i3−i3i3−i30000
χ8466-6-6-36-6−6i6i−6i6i33-33i−3i3i−3i-330000000000000000000000000000003−33−300000000000000000000000000000003−3i3−i3i3−i30000
χ8566-6-6-36-6−6i6i−6i6i33-33i−3i3i−3i-33000000000000000000000000000000−33−330000000000000000000000000000000−33−i3i3−i3i30000
χ8666-6-6-3-666i−6i−6i6i33-3−3i3i3i−3i3-30000000000000000000000000000003−33−30000000000000000000000000000000−33−i3i3i3−i30000
χ8766-6-6-3-666i−6i−6i6i33-3−3i3i3i−3i3-3000000000000000000000000000000−33−3300000000000000000000000000000003−3i3−i3−i3i30000
χ8866-6-6-3-66−6i6i6i−6i33-33i−3i−3i3i3-30000000000000000000000000000003−33−30000000000000000000000000000000−33i3−i3−i3i30000
χ8966-6-6-3-66−6i6i6i−6i33-33i−3i−3i3i3-3000000000000000000000000000000−33−3300000000000000000000000000000003−3−i3i3i3−i30000
χ908-88-880000008-8-8000000-4-444-4-44422-2-2000000000000000000000000000000000000000000000000000000000000000
χ918-8-888000000-88-8000000-4-44444-4-42-2-22000000000000000000000000000000000000000000000000000000000000000
χ9212-1212-12-6000000-6660000000000000000000000000000004-40000-2-22200000000000000000000000000000000000000000
χ9312-1212-12-6000000-666000000000000000000000000000000-44000022-2-200000000000000000000000000000000000000000
χ9412-12-1212-60000006-6600000000000000000000000000000000000023−23−232300000000000000000000000000000000000000000
χ9512-12-1212-60000006-66000000000000000000000000000000000000−232323−2300000000000000000000000000000000000000000

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