Finite Group Databasebeta

← Group #13149553

Character table — Group #13149553

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size111122222222224444446666666612121212121212121212121212121212181818181818181818181818181818181818242424242424363636363636363636363636363636363636363636363636363636
order12223444444666121212121212336666663666121212121212121212121212224444666612121212121212121212121212122444444446612121212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-111-11-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ311111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-11-111-1-1111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ51111111-1-1-1-111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1111111111111111111-1-111-1-1-11-11-1-1-11-1-1-1-1-111-1-1-1-111-1-111-1-1
χ61111111-1-1-1-111111-1-1-1-111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11-111-11-1-111111-1-111-1-1-1-11111-1-1
χ71111111-1-1-1-111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11-11-11-111-111-1-111-1-111-1-111-1-111
χ81111111-1-1-1-111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-11-1-1111-11-1-111-1-1111111-1-1-1-111
χ911111-1-111-1-1111-1-111-1-1111111111111-1-111-1-1-1-1-1-111111111111111111111-1-1-1-111-1-11-11-1-1-11-1-1-1-1-1-111-1-1-1-111-1-111
χ1011111-1-111-1-1111-1-111-1-1111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11-1111111-1-1-1-111-1-1-1-111
χ1111111-1-111-1-1111-1-111-1-1111111111111-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-11-1-11-1111-1-1-1-1111111-1-111-1-1
χ1211111-1-111-1-1111-1-111-1-1111111111111-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1111-1-1-11111-1-111-1-11111-1-1
χ1311111-1-1-1-111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-11-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1
χ1411111-1-1-1-111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1111-1-1-1-11111111111-1-1-1-1
χ1511111-1-1-1-111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-111111-1-1-1-1-111-1-1-1-1-1-111111111
χ1611111-1-1-1-111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-111-1-11111-1-11111-1-1-1-1-1-11111
χ17222222222222222222222-12-12-1-12-1-1-1-1-1-1-1-122-1-1222200002200000000-1-1-1-1-1-1-1-1-1-1222000000-1-100000000-1-1-1-10000
χ18222222222222222222222-12-12-1-12-1-1-1-1-1-1-1-122-1-122220000-2-2000000001111-1-1-1-1-1-1-2-2-2000000110000000011110000
χ1922222222222222222222-12-12-122-1-1-1-1-12222-1-122-1-1-1-1220000-1-1-1-100000000-1-1-1-1-1-100022020000000000-1-10000-1-1-1-1
χ2022222222222222222222-12-12-122-1-1-1-1-12222-1-122-1-1-1-1-2-20000111100000000-1-1-1-1-1-1000-2-20-200000000001100001111
χ212222222-2-2-2-222222-2-2-2-22-12-12-1-12-1-1-1-1-1-111-2-21122-2-200002200000000-1-1-1-111-1-111-22-20000001100000000-1-1110000
χ222222222-2-2-2-222222-2-2-2-22-12-12-1-12-1-1-1-1-1-111-2-21122-2-20000-2-200000000111111-1-1112-22000000-1-10000000011-1-10000
χ232222222-2-2-2-222222-2-2-2-2-12-12-122-1-1-1-1-122-2-211-2-2-1-111220000-1-1-1-10000000011-1-1110002-20-20000000000110000-1-111
χ242222222-2-2-2-222222-2-2-2-2-12-12-122-1-1-1-1-122-2-211-2-2-1-111-2-2000011110000000011-1-111000-22020000000000-1-1000011-1-1
χ2522222-2-222-2-2222-2-222-2-22-12-12-1-12-1-1-1-111-1-1-2-211-2-22200002200000000-1-1-1-11111-1-1-2-22000000110000000011-1-10000
χ2622222-2-222-2-2222-2-222-2-22-12-12-1-12-1-1-1-111-1-1-2-211-2-2220000-2-20000000011111111-1-122-2000000-1-100000000-1-1110000
χ2722222-2-222-2-2222-2-222-2-2-12-12-122-1-1-1-1-1-2-22211-2-211-1-1220000-1-1-1-1000000001111-1-1000-220-2000000000011000011-1-1
χ2822222-2-222-2-2222-2-222-2-2-12-12-122-1-1-1-1-1-2-22211-2-211-1-1-2-200001111000000001111-1-10002-2020000000000-1-10000-1-111
χ2922222-2-2-2-222222-2-2-2-2222-12-12-1-12-1-1-1-1111122-1-1-2-2-2-200002200000000-1-1-1-1-1-111112-2-2000000-1-10000000011110000
χ3022222-2-2-2-222222-2-2-2-2222-12-12-1-12-1-1-1-1111122-1-1-2-2-2-20000-2-2000000001111-1-11111-2220000001100000000-1-1-1-10000
χ3122222-2-2-2-222222-2-2-2-222-12-12-122-1-1-1-1-1-2-2-2-2-1-1221111220000-1-1-1-100000000-1-11111000-2-2020000000000-1-100001111
χ3222222-2-2-2-222222-2-2-2-222-12-12-122-1-1-1-1-1-2-2-2-2-1-1221111-2-20000111100000000-1-11111000220-20000000000110000-1-1-1-1
χ332-22-22000000-22-200000022-22-2-2-222-2-220000000000002-22i−2i2i−2i22-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000
χ342-22-22000000-22-200000022-22-2-2-222-2-220000000000002-2−2i2i−2i2i22-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000
χ352-22-22000000-22-200000022-22-2-2-222-2-22000000000000-222i−2i−2i2i-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000
χ362-22-22000000-22-200000022-22-2-2-222-2-22000000000000-22−2i2i2i−2i-2-222−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000
χ372-2-2222i−2i2i−2i2-2-2-222i−2i2i−2i2-222-2-222-2-22-22-22i−2i2i−2i2-22-22i−2i2i−2i0000000000000000002-22i−2i2i−2i000000000000000000000000000
χ382-2-2222i−2i2i−2i2-2-2-222i−2i2i−2i2-22-1-212-11-2-11-11−ii−ii2-2-112i−2i2i−2i00000000000000−i3i3−i3i3-11−ii−ii000000000−i3i3000000003−33−30000
χ392-2-2222i−2i2i−2i2-2-2-222i−2i2i−2i2-22-1-212-11-2-11-11−ii−ii2-2-112i−2i2i−2i00000000000000i3−i3i3−i3-11−ii−ii000000000i3−i300000000−33−330000
χ402-2-2222i−2i2i−2i2-2-2-222i−2i2i−2i2-2-121-2-12-21-11-112i−2i2i−2i-112-2−ii−ii000000−i3i3−i3i300000000-11−ii−ii00000000000000000−i3i300003−33−3
χ412-2-2222i−2i2i−2i2-2-2-222i−2i2i−2i2-2-121-2-12-21-11-112i−2i2i−2i-112-2−ii−ii000000i3−i3i3−i300000000-11−ii−ii00000000000000000i3−i30000−33−33
χ422-2-2222i−2i−2i2i-22-2-222i−2i−2i2i-2222-2-222-2-22-22-22i−2i−2i2i-22-222i−2i−2i2i000000000000000000-222i−2i−2i2i000000000000000000000000000
χ432-2-2222i−2i−2i2i-22-2-222i−2i−2i2i-222-1-212-11-2-11-11−iii−i-221-12i−2i−2i2i00000000000000−i3i3−i3i31-1−iii−i000000000i3−i3000000003−3−330000
χ442-2-2222i−2i−2i2i-22-2-222i−2i−2i2i-222-1-212-11-2-11-11−iii−i-221-12i−2i−2i2i00000000000000i3−i3i3−i31-1−iii−i000000000−i3i300000000−333−30000
χ452-2-2222i−2i−2i2i-22-2-222i−2i−2i2i-22-121-2-12-21-11-112i−2i−2i2i1-1-22−iii−i000000−i3i3−i3i3000000001-1−iii−i00000000000000000i3−i300003−3−33
χ462-2-2222i−2i−2i2i-22-2-222i−2i−2i2i-22-121-2-12-21-11-112i−2i−2i2i1-1-22−iii−i000000i3−i3i3−i3000000001-1−iii−i00000000000000000−i3i30000−333−3
χ472-2-222−2i2i2i−2i-22-2-22−2i2i2i−2i-2222-2-222-2-22-22-2−2i2i2i−2i-22-22−2i2i2i−2i000000000000000000-22−2i2i2i−2i000000000000000000000000000
χ482-2-222−2i2i2i−2i-22-2-22−2i2i2i−2i-222-1-212-11-2-11-11i−i−ii-221-1−2i2i2i−2i00000000000000−i3i3−i3i31-1i−i−ii000000000i3−i300000000−333−30000
χ492-2-222−2i2i2i−2i-22-2-22−2i2i2i−2i-222-1-212-11-2-11-11i−i−ii-221-1−2i2i2i−2i00000000000000i3−i3i3−i31-1i−i−ii000000000−i3i3000000003−3−330000
χ502-2-222−2i2i2i−2i-22-2-22−2i2i2i−2i-22-121-2-12-21-11-11−2i2i2i−2i1-1-22i−i−ii000000−i3i3−i3i3000000001-1i−i−ii00000000000000000i3−i30000−333−3
χ512-2-222−2i2i2i−2i-22-2-22−2i2i2i−2i-22-121-2-12-21-11-11−2i2i2i−2i1-1-22i−i−ii000000i3−i3i3−i3000000001-1i−i−ii00000000000000000−i3i300003−3−33
χ522-2-222−2i2i−2i2i2-2-2-22−2i2i−2i2i2-222-2-222-2-22-22-2−2i2i−2i2i2-22-2−2i2i−2i2i0000000000000000002-2−2i2i−2i2i000000000000000000000000000
χ532-2-222−2i2i−2i2i2-2-2-22−2i2i−2i2i2-22-1-212-11-2-11-11i−ii−i2-2-11−2i2i−2i2i00000000000000−i3i3−i3i3-11i−ii−i000000000−i3i300000000−33−330000
χ542-2-222−2i2i−2i2i2-2-2-22−2i2i−2i2i2-22-1-212-11-2-11-11i−ii−i2-2-11−2i2i−2i2i00000000000000i3−i3i3−i3-11i−ii−i000000000i3−i3000000003−33−30000
χ552-2-222−2i2i−2i2i2-2-2-22−2i2i−2i2i2-2-121-2-12-21-11-11−2i2i−2i2i-112-2i−ii−i000000−i3i3−i3i300000000-11i−ii−i00000000000000000−i3i30000−33−33
χ562-2-222−2i2i−2i2i2-2-2-22−2i2i−2i2i2-2-121-2-12-21-11-11−2i2i−2i2i-112-2i−ii−i000000i3−i3i3−i300000000-11i−ii−i00000000000000000i3−i300003−33−3
χ5744444444444444444444-2-2-2-2-2-2-2-21111-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000111111000000000000000000000000000
χ584444444-4-4-4-444444-4-4-4-4-2-2-2-2-2-2-2-21111-2-2222222-2-222000000000000000000-1-111-1-1000000000000000000000000000
χ5944444-4-444-4-4444-4-444-4-4-2-2-2-2-2-2-2-2111122-2-2222222-2-2000000000000000000-1-1-1-111000000000000000000000000000
χ6044444-4-4-4-444444-4-4-4-444-2-2-2-2-2-2-2-211112222-2-2-2-2222200000000000000000011-1-1-1-1000000000000000000000000000
χ6144-4-440000004-4-4000000444-4-4-44-444-4-4000000000000000000000000000000000000000000000000000000000000000
χ6244-4-440000004-4-40000004-242-42-2-4-2-2220000000000000000000000000023−23−2323000000000000000000000000000000000
χ6344-4-440000004-4-40000004-242-42-2-4-2-22200000000000000000000000000−232323−23000000000000000000000000000000000
χ6444-4-440000004-4-4000000-24-2-42-442-2-222000000000000000000−2i32i32i3−2i300000000000000000000000000000000000000000
χ6544-4-440000004-4-4000000-24-2-42-442-2-2220000000000000000002i3−2i3−2i32i300000000000000000000000000000000000000000
χ664-44-44000000-44-40000004-2-4-2-4224-222-200000000000000004i−4i00000000−2i−2i2i2i000000000000000000000000000000000
χ674-44-44000000-44-40000004-2-4-2-4224-222-20000000000000000−4i4i000000002i2i−2i−2i000000000000000000000000000000000
χ684-44-44000000-44-4000000-24242-4-4-2-222-20000000000004-40000-2-22200000000000000000000000000000000000000000
χ694-44-44000000-44-4000000-24242-4-4-2-222-2000000000000-44000022-2-200000000000000000000000000000000000000000
χ704-4-4444i−4i4i−4i4-4-4-444i−4i4i−4i4-4-2-222-2-2221-11-1−2i2i−2i2i-22-22−2i2i−2i2i0000000000000000001-1i−ii−i000000000000000000000000000
χ714-4-4444i−4i−4i4i-44-4-444i−4i−4i4i-44-2-222-2-2221-11-1−2i2i2i−2i2-22-2−2i2i2i−2i000000000000000000-11i−i−ii000000000000000000000000000
χ724-4-444−4i4i4i−4i-44-4-44−4i4i4i−4i-44-2-222-2-2221-11-12i−2i−2i2i2-22-22i−2i−2i2i000000000000000000-11−iii−i000000000000000000000000000
χ734-4-444−4i4i−4i4i4-4-4-44−4i4i−4i4i4-4-2-222-2-2221-11-12i−2i2i−2i-22-222i−2i2i−2i0000000000000000001-1−ii−ii000000000000000000000000000
χ746666-3666666-3-3-3-3-3-3-3-3-30000000000000000000000000022000000-1-1-1-1000000000000000202200-1-1-1-1-1-10000000000
χ756666-3666666-3-3-3-3-3-3-3-3-300000000000000000000000000-2-20000001111000000000000000-20-2-2001111110000000000
χ766666-366-6-6-6-6-3-3-3-3-333330000000000000000000000000022000000-1-1-1-1000000000000000-202-20011-1-1110000000000
χ776666-366-6-6-6-6-3-3-3-3-3333300000000000000000000000000-2-2000000111100000000000000020-2200-1-111-1-10000000000
χ786666-3-6-666-6-6-3-3-333-3-3330000000000000000000000000022000000-1-1-1-1000000000000000-20-22001111-1-10000000000
χ796666-3-6-666-6-6-3-3-333-3-33300000000000000000000000000-2-20000001111000000000000000202-200-1-1-1-1110000000000
χ806666-3-6-6-6-666-3-3-33333-3-30000000000000000000000000022000000-1-1-1-100000000000000020-2-200-1-111110000000000
χ816666-3-6-6-6-666-3-3-33333-3-300000000000000000000000000-2-20000001111000000000000000-20220011-1-1-1-10000000000
χ826-6-66-36i−6i6i−6i6-633-3−3i3i−3i3i-3300000000000000000000000000000000003−33−30000000000000000000003−3−i3i3−i3i30000000000
χ836-6-66-36i−6i6i−6i6-633-3−3i3i−3i3i-330000000000000000000000000000000000−33−33000000000000000000000−33i3−i3i3−i30000000000
χ846-6-66-36i−6i−6i6i-6633-3−3i3i3i−3i3-300000000000000000000000000000000003−33−3000000000000000000000−33−i3i3i3−i30000000000
χ856-6-66-36i−6i−6i6i-6633-3−3i3i3i−3i3-30000000000000000000000000000000000−33−330000000000000000000003−3i3−i3−i3i30000000000
χ866-6-66-3−6i6i6i−6i-6633-33i−3i−3i3i3-300000000000000000000000000000000003−33−3000000000000000000000−33i3−i3−i3i30000000000
χ876-6-66-3−6i6i6i−6i-6633-33i−3i−3i3i3-30000000000000000000000000000000000−33−330000000000000000000003−3−i3i3i3−i30000000000
χ886-6-66-3−6i6i−6i6i6-633-33i−3i3i−3i-3300000000000000000000000000000000003−33−30000000000000000000003−3i3−i3i3−i30000000000
χ896-6-66-3−6i6i−6i6i6-633-33i−3i3i−3i-330000000000000000000000000000000000−33−33000000000000000000000−33−i3i3−i3i30000000000
χ9088-8-880000008-8-8000000-4-4-4444-4422-2-2000000000000000000000000000000000000000000000000000000000000000
χ918-88-88000000-88-8000000-4-44-4444-42-2-22000000000000000000000000000000000000000000000000000000000000000
χ921212-12-12-6000000-6660000000000000000000000000000000000000000−2i32i32i3−2i30000000000000000000000000000000000000
χ931212-12-12-6000000-66600000000000000000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000000000000
χ9412-1212-12-60000006-66000000000000000000000000000000004i−4i000000−2i−2i2i2i0000000000000000000000000000000000000
χ9512-1212-12-60000006-6600000000000000000000000000000000−4i4i0000002i2i−2i−2i0000000000000000000000000000000000000

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