Finite Group Databasebeta

← Group #13149561

Character table — Group #13149561

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size111122222222224444446666666612121212121212121212121212121212181818181818181818181818181818181818242424242424363636363636363636363636363636363636363636363636363636
order1222344444466612121212121233666666366612121212121212121212121222444466661212121212121212121212121212222444444666666121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-11-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111
χ311111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111111111111-1-1-111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1111111-111-1-1-11-1-11111-1-111-1-1-1-1-1-1-1-1-1-1
χ51111111-1-1-1-111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-11-1-11-1-11-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ61111111-1-1-1-111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-111111-1-1-11111-1-1-1-1111111-1-1-1-1
χ71111111-1-1-1-111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ81111111-1-1-1-111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-111111111
χ911111-1-111-1-1111-1-111-1-111111111111111-1-1-1-1-1-111-1-1111111111111111111-1-111-1-1-11-1-11-1-11-111-1-1-1-1-1-1-1-111-1-111-1-1
χ1011111-1-111-1-1111-1-111-1-111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11-11-1-1111-1-1-1111111-1-1-1-11111-1-1
χ1111111-1-111-1-1111-1-111-1-111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111-11-11-1-111-1-1111111-1-1-1-111
χ1211111-1-111-1-1111-1-111-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-111-11-11-1-1111-1-111-1-111-1-111-1-111
χ1311111-1-1-1-111111-1-1-1-111111111111111-1-111-1-1-1-1-1-111111111111111111111-1-1-1-111-1-11-1-11-1-11-1-111-1-1-1-1-1-1-1-111-1-111
χ1411111-1-1-1-111111-1-1-1-111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-11-1111-1-11111-1-111-1-1-1-111
χ1511111-1-1-1-111111-1-1-1-111111111111111-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-11-11-1111-111-1-1-1-11111-1-11111-1-1
χ1611111-1-1-1-111111-1-1-1-111111111111111-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111-1111-1-11-1-1-11111-1-11111-1-111-1-1
χ17222222222222222222222-12-12-1-12-1-1-1-1-1-1-1-122-1-1222200220000000000-1-1-1-1-1-1-1-1-1-12000220000000-1-10000-1-1-1-10000
χ18222222222222222222222-12-12-1-12-1-1-1-1-1-1-1-122-1-1222200-2-200000000001111-1-1-1-1-1-1-2000-2-2000000011000011110000
χ1922222222222222222222-12-12-122-1-1-1-1-12222-1-122-1-1-1-1220000-1-1-1-100000000-1-1-1-1-1-100020002200000000-1-10000-1-1-1-1
χ2022222222222222222222-12-12-122-1-1-1-1-12222-1-122-1-1-1-1-2-20000111100000000-1-1-1-1-1-1000-2000-2-2000000001100001111
χ212222222-2-2-2-222222-2-2-2-22-12-12-1-12-1-1-1-1111122-1-1-2-2-2-200220000000000-1-1-1-1-1-111112000-2-20000000-1-1000011110000
χ222222222-2-2-2-222222-2-2-2-22-12-12-1-12-1-1-1-1111122-1-1-2-2-2-200-2-200000000001111-1-11111-2000220000000110000-1-1-1-10000
χ232222222-2-2-2-222222-2-2-2-2-12-12-122-1-1-1-1-1-2-2-2-2-1-1221111220000-1-1-1-100000000-1-111110002000-2-200000000-1-100001111
χ242222222-2-2-2-222222-2-2-2-2-12-12-122-1-1-1-1-1-2-2-2-2-1-1221111-2-20000111100000000-1-11111000-20002200000000110000-1-1-1-1
χ2522222-2-222-2-2222-2-222-2-22-12-12-1-12-1-1-1-1-1-111-2-21122-2-200220000000000-1-1-1-111-1-111-20002-20000000110000-1-1110000
χ2622222-2-222-2-2222-2-222-2-22-12-12-1-12-1-1-1-1-1-111-2-21122-2-200-2-20000000000111111-1-1112000-220000000-1-1000011-1-10000
χ2722222-2-222-2-2222-2-222-2-2-12-12-122-1-1-1-1-122-2-211-2-2-1-111220000-1-1-1-10000000011-1-111000-20002-200000000110000-1-111
χ2822222-2-222-2-2222-2-222-2-2-12-12-122-1-1-1-1-122-2-211-2-2-1-111-2-2000011110000000011-1-1110002000-2200000000-1-1000011-1-1
χ2922222-2-2-2-222222-2-2-2-2222-12-12-1-12-1-1-1-111-1-1-2-211-2-22200220000000000-1-1-1-11111-1-1-2000-22000000011000011-1-10000
χ3022222-2-2-2-222222-2-2-2-2222-12-12-1-12-1-1-1-111-1-1-2-211-2-22200-2-2000000000011111111-1-120002-20000000-1-10000-1-1110000
χ3122222-2-2-2-222222-2-2-2-222-12-12-122-1-1-1-1-1-2-22211-2-211-1-1220000-1-1-1-1000000001111-1-1000-2000-220000000011000011-1-1
χ3222222-2-2-2-222222-2-2-2-222-12-12-122-1-1-1-1-1-2-22211-2-211-1-1-2-200001111000000001111-1-100020002-200000000-1-10000-1-111
χ3322-2-222-22i−2i2i−2i2-2-22-22i−2i2i−2i22-2-222-2-22-22-22i−2i2i−2i2-22-22i−2i2i−2i0000000000000000002-22i−2i2i−2i000000000000000000000000000
χ3422-2-222-22i−2i2i−2i2-2-22-22i−2i2i−2i2-1-212-11-2-11-11−ii−ii2-2-112i−2i2i−2i00000000000000−i3−i3i3i3-11−ii−ii0000000000000−i3i300003−33−30000
χ3522-2-222-22i−2i2i−2i2-2-22-22i−2i2i−2i2-1-212-11-2-11-11−ii−ii2-2-112i−2i2i−2i00000000000000i3i3−i3−i3-11−ii−ii0000000000000i3−i30000−33−330000
χ3622-2-222-22i−2i2i−2i2-2-22-22i−2i2i−2i-121-2-12-21-11-112i−2i2i−2i-112-2−ii−ii000000−i3−i3i3i300000000-11−ii−ii00000000000000000−i3i300003−33−3
χ3722-2-222-22i−2i2i−2i2-2-22-22i−2i2i−2i-121-2-12-21-11-112i−2i2i−2i-112-2−ii−ii000000i3i3−i3−i300000000-11−ii−ii00000000000000000i3−i30000−33−33
χ3822-2-222-2−2i2i−2i2i2-2-22-2−2i2i−2i2i22-2-222-2-22-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000000000000000002-2−2i2i−2i2i000000000000000000000000000
χ3922-2-222-2−2i2i−2i2i2-2-22-2−2i2i−2i2i2-1-212-11-2-11-11i−ii−i2-2-11−2i2i−2i2i00000000000000−i3−i3i3i3-11i−ii−i0000000000000−i3i30000−33−330000
χ4022-2-222-2−2i2i−2i2i2-2-22-2−2i2i−2i2i2-1-212-11-2-11-11i−ii−i2-2-11−2i2i−2i2i00000000000000i3i3−i3−i3-11i−ii−i0000000000000i3−i300003−33−30000
χ4122-2-222-2−2i2i−2i2i2-2-22-2−2i2i−2i2i-121-2-12-21-11-11−2i2i−2i2i-112-2i−ii−i000000−i3−i3i3i300000000-11i−ii−i00000000000000000−i3i30000−33−33
χ4222-2-222-2−2i2i−2i2i2-2-22-2−2i2i−2i2i-121-2-12-21-11-11−2i2i−2i2i-112-2i−ii−i000000i3i3−i3−i300000000-11i−ii−i00000000000000000i3−i300003−33−3
χ4322-2-22-222i−2i−2i2i2-2-2-222i−2i−2i2i22-2-222-2-22-22-22i−2i−2i2i-22-222i−2i−2i2i000000000000000000-222i−2i−2i2i000000000000000000000000000
χ4422-2-22-222i−2i−2i2i2-2-2-222i−2i−2i2i2-1-212-11-2-11-11−iii−i-221-12i−2i−2i2i00000000000000−i3−i3i3i31-1−iii−i0000000000000i3−i300003−3−330000
χ4522-2-22-222i−2i−2i2i2-2-2-222i−2i−2i2i2-1-212-11-2-11-11−iii−i-221-12i−2i−2i2i00000000000000i3i3−i3−i31-1−iii−i0000000000000−i3i30000−333−30000
χ4622-2-22-222i−2i−2i2i2-2-2-222i−2i−2i2i-121-2-12-21-11-112i−2i−2i2i1-1-22−iii−i000000−i3−i3i3i3000000001-1−iii−i00000000000000000i3−i300003−3−33
χ4722-2-22-222i−2i−2i2i2-2-2-222i−2i−2i2i-121-2-12-21-11-112i−2i−2i2i1-1-22−iii−i000000i3i3−i3−i3000000001-1−iii−i00000000000000000−i3i30000−333−3
χ4822-2-22-22−2i2i2i−2i2-2-2-22−2i2i2i−2i22-2-222-2-22-22-2−2i2i2i−2i-22-22−2i2i2i−2i000000000000000000-22−2i2i2i−2i000000000000000000000000000
χ4922-2-22-22−2i2i2i−2i2-2-2-22−2i2i2i−2i2-1-212-11-2-11-11i−i−ii-221-1−2i2i2i−2i00000000000000−i3−i3i3i31-1i−i−ii0000000000000i3−i30000−333−30000
χ5022-2-22-22−2i2i2i−2i2-2-2-22−2i2i2i−2i2-1-212-11-2-11-11i−i−ii-221-1−2i2i2i−2i00000000000000i3i3−i3−i31-1i−i−ii0000000000000−i3i300003−3−330000
χ5122-2-22-22−2i2i2i−2i2-2-2-22−2i2i2i−2i-121-2-12-21-11-11−2i2i2i−2i1-1-22i−i−ii000000−i3−i3i3i3000000001-1i−i−ii00000000000000000i3−i30000−333−3
χ5222-2-22-22−2i2i2i−2i2-2-2-22−2i2i2i−2i-121-2-12-21-11-11−2i2i2i−2i1-1-22i−i−ii000000i3i3−i3−i3000000001-1i−i−ii00000000000000000−i3i300003−3−33
χ532-22-22000000-22-2000000222-2-2-22-222-2-20000000000002-22i−2i2i−2i2-22-22i2i−2i−2i2i−2i2i−2i000000000000000000000000000000000
χ542-22-22000000-22-2000000222-2-2-22-222-2-20000000000002-2−2i2i−2i2i2-22-2−2i−2i2i2i−2i2i−2i2i000000000000000000000000000000000
χ552-22-22000000-22-2000000222-2-2-22-222-2-2000000000000-222i−2i−2i2i-22-22−2i−2i2i2i2i−2i2i−2i000000000000000000000000000000000
χ562-22-22000000-22-2000000222-2-2-22-222-2-2000000000000-22−2i2i2i−2i-22-222i2i−2i−2i−2i2i−2i2i000000000000000000000000000000000
χ5744444444444444444444-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000111111000000000000000000000000000
χ584444444-4-4-4-444444-4-4-4-4-2-2-2-2-2-2-2-211112222-2-2-2-2222200000000000000000011-1-1-1-1000000000000000000000000000
χ5944444-4-444-4-4444-4-444-4-4-2-2-2-2-2-2-2-21111-2-2222222-2-222000000000000000000-1-111-1-1000000000000000000000000000
χ6044444-4-4-4-444444-4-4-4-444-2-2-2-2-2-2-2-2111122-2-2222222-2-2000000000000000000-1-1-1-111000000000000000000000000000
χ6144-4-444-44i−4i4i−4i4-4-44-44i−4i4i−4i-2-222-2-2221-11-1−2i2i−2i2i-22-22−2i2i−2i2i0000000000000000001-1i−ii−i000000000000000000000000000
χ6244-4-444-4−4i4i−4i4i4-4-44-4−4i4i−4i4i-2-222-2-2221-11-12i−2i2i−2i-22-222i−2i2i−2i0000000000000000001-1−ii−ii000000000000000000000000000
χ6344-4-44-444i−4i−4i4i4-4-4-444i−4i−4i4i-2-222-2-2221-11-1−2i2i2i−2i2-22-2−2i2i2i−2i000000000000000000-11i−i−ii000000000000000000000000000
χ6444-4-44-44−4i4i4i−4i4-4-4-44−4i4i4i−4i-2-222-2-2221-11-12i−2i−2i2i2-22-22i−2i−2i2i000000000000000000-11−iii−i000000000000000000000000000
χ654-44-44000000-44-40000004-242-42-2-4-2-222000000000000004i−4i0000000000−2i2i−2i2i000000000000000000000000000000000
χ664-44-44000000-44-40000004-242-42-2-4-2-22200000000000000−4i4i00000000002i−2i2i−2i000000000000000000000000000000000
χ674-44-44000000-44-4000000-24-2-42-442-2-2220000000000004-40000-22-2200000000000000000000000000000000000000000
χ684-44-44000000-44-4000000-24-2-42-442-2-222000000000000-4400002-22-200000000000000000000000000000000000000000
χ694-4-444000000-4-4400000044-44-4-4-444-4-44000000000000000000000000000000000000000000000000000000000000000
χ704-4-444000000-4-440000004-2-4-2-4224-222-20000000000000000000000000023−23−2323000000000000000000000000000000000
χ714-4-444000000-4-440000004-2-4-2-4224-222-200000000000000000000000000−232323−23000000000000000000000000000000000
χ724-4-444000000-4-44000000-24242-4-4-2-222-2000000000000000000−2i32i32i3−2i300000000000000000000000000000000000000000
χ734-4-444000000-4-44000000-24242-4-4-2-222-20000000000000000002i3−2i3−2i32i300000000000000000000000000000000000000000
χ746666-3666666-3-3-3-3-3-3-3-3-30000000000000000000000000000220000-1-1-1-10000000000022000200-1-1-1-100-1-10000000000
χ756666-3666666-3-3-3-3-3-3-3-3-30000000000000000000000000000-2-20000111100000000000-2-2000-200111100110000000000
χ766666-366-6-6-6-6-3-3-3-3-333330000000000000000000000000000220000-1-1-1-100000000000-2-2000200111100-1-10000000000
χ776666-366-6-6-6-6-3-3-3-3-333330000000000000000000000000000-2-2000011110000000000022000-200-1-1-1-100110000000000
χ786666-3-6-666-6-6-3-3-333-3-3330000000000000000000000000000220000-1-1-1-1000000000002-2000-200-1-11100110000000000
χ796666-3-6-666-6-6-3-3-333-3-3330000000000000000000000000000-2-20000111100000000000-2200020011-1-100-1-10000000000
χ806666-3-6-6-6-666-3-3-33333-3-30000000000000000000000000000220000-1-1-1-100000000000-22000-20011-1-100110000000000
χ816666-3-6-6-6-666-3-3-33333-3-30000000000000000000000000000-2-200001111000000000002-2000200-1-11100-1-10000000000
χ8266-6-6-36-66i−6i6i−6i-333-33−3i3i−3i3i00000000000000000000000000000000003−33−30000000000000000000−i3i3−i3i3003−30000000000
χ8366-6-6-36-66i−6i6i−6i-333-33−3i3i−3i3i0000000000000000000000000000000000−33−330000000000000000000i3−i3i3−i300−330000000000
χ8466-6-6-36-6−6i6i−6i6i-333-333i−3i3i−3i00000000000000000000000000000000003−33−30000000000000000000i3−i3i3−i3003−30000000000
χ8566-6-6-36-6−6i6i−6i6i-333-333i−3i3i−3i0000000000000000000000000000000000−33−330000000000000000000−i3i3−i3i300−330000000000
χ8666-6-6-3-666i−6i−6i6i-3333-3−3i3i3i−3i00000000000000000000000000000000003−33−30000000000000000000−i3i3i3−i300−330000000000
χ8766-6-6-3-666i−6i−6i6i-3333-3−3i3i3i−3i0000000000000000000000000000000000−33−330000000000000000000i3−i3−i3i3003−30000000000
χ8866-6-6-3-66−6i6i6i−6i-3333-33i−3i−3i3i00000000000000000000000000000000003−33−30000000000000000000i3−i3−i3i300−330000000000
χ8966-6-6-3-66−6i6i6i−6i-3333-33i−3i−3i3i0000000000000000000000000000000000−33−330000000000000000000−i3i3i3−i3003−30000000000
χ908-88-88000000-88-8000000-4-4-4444-4422-2-2000000000000000000000000000000000000000000000000000000000000000
χ918-8-888000000-8-88000000-4-44-4444-42-2-22000000000000000000000000000000000000000000000000000000000000000
χ9212-1212-12-60000006-6600000000000000000000000000000000004i−4i0000−2i−2i2i2i0000000000000000000000000000000000000
χ9312-1212-12-60000006-660000000000000000000000000000000000−4i4i00002i2i−2i−2i0000000000000000000000000000000000000
χ9412-12-1212-600000066-60000000000000000000000000000000000000000−2i32i32i3−2i30000000000000000000000000000000000000
χ9512-12-1212-600000066-600000000000000000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000000000000

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