Finite Group Databasebeta

← Group #13148700

Character table — Group #13148700

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size111122222222224444446666666612121212121212121212121212121212181818181818181818181818181818181818242424242424363636363636363636363636363636363636363636363636363636
order122222344446666612121212336666663666666612121212121212124444441212121212121212121212126612121212222444444666666121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111-1-111-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-1
χ311111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1111111-11-1-1-11-11-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-11-1-1-11-11-1-1-1-111-1-1-1-1-1-111-1-111
χ51111111-1-1-1-111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-11-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111
χ61111111-1-1-1-111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1111-111-1-111-1-11111-1-1-1-11111-1-1
χ71111111-1-1-1-111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11-11-11-111-1-1-11111-1-1111111-1-1-1-1
χ81111111-1-1-1-111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111111-1-111-1-111-1-1-1-111
χ91111-1-1111-1-1111-1-111-1-1111111111-1-1-1-111111-1-111-1-1111111111111111111-1-111-1-11-1-1-1-111-1-1-1-111-1-111-1-1-1-111-1-1-1-1
χ101111-1-1111-1-1111-1-111-1-1111111111-1-1-1-111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1111-1-1-1-111111111-1-111-1-1-1-1-1-111
χ111111-1-1111-1-1111-1-111-1-1111111111-1-1-1-111111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11-1-1-1-11111-1-111-1-11111
χ121111-1-1111-1-1111-1-111-1-1111111111-1-1-1-111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-11-111-111-111-1-1-1-1-1-111111111-1-1
χ131111-1-11-1-111111-1-1-1-111111111111-1-1-1-1111-1-111-1-111111111111111111111-1-1-1-111-111-11-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1
χ141111-1-11-1-111111-1-1-1-111111111111-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-1-1-111111111-1-111
χ151111-1-11-1-111111-1-1-1-111111111111-1-1-1-1111-1-111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-11-111111-1-1-1-1-1-1-1-1111111
χ161111-1-11-1-111111-1-1-1-111111111111-1-1-1-1111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111-111-11-11-1-1-111111111-1-1-1-111-1-1
χ17222222222222222222222-12-12-12-1-122-1-1-1-1-122-1-1-1-1222200000000-1-1-1-10000-1-1-1-1-1-120022000000-1-1000000-1-100-1-100
χ18222222222222222222222-12-12-12-1-122-1-1-1-1-122-1-1-1-122-2-20000000011110000-1-1-1-1-1-1-200-2-20000001100000011001100
χ1922222222222222222222-12-12-12-12-1-1-122-1-1-1-1-12222-1-100002200000000-1-1-1-1-1-1-1-1-1-10020002020000-1-1000000-1-100-1-1
χ2022222222222222222222-12-12-12-12-1-1-122-1-1-1-1-12222-1-10000-2-2000000001111-1-1-1-1-1-100-2000-20-2000011000000110011
χ212222222-2-2-2-222222-2-2-2-22-12-12-12-1-122-1-1-1-1-1-2-21111-2-22200000000-1-1-1-10000-1-11111-2002-2000000110000001100-1-100
χ222222222-2-2-2-222222-2-2-2-22-12-12-12-1-122-1-1-1-1-1-2-21111-2-2-2-20000000011110000-1-11111200-22000000-1-1000000-1-1001100
χ232222222-2-2-2-222222-2-2-2-2-12-12-12-12-1-1-122-1-1-111-2-2-2-21100002200000000-1-1-1-1-1-1111100-2000-2020000110000001100-1-1
χ242222222-2-2-2-222222-2-2-2-2-12-12-12-12-1-1-122-1-1-111-2-2-2-2110000-2-2000000001111-1-1111100200020-20000-1-1000000-1-10011
χ252222-2-2222-2-2222-2-222-2-22-12-12-12-1-1-2-211-1-1-12211-1-1-2-22200000000-1-1-1-1000011-1-111200-2-2000000-1-100000011001100
χ262222-2-2222-2-2222-2-222-2-22-12-12-12-1-1-2-211-1-1-12211-1-1-2-2-2-2000000001111000011-1-111-2002200000011000000-1-100-1-100
χ272222-2-2222-2-2222-2-222-2-2-12-12-12-12-111-2-2-1-1-1-1-1-2-2221100002200000000-1-1-1-111-1-11100-200020-2000011000000-1-10011
χ282222-2-2222-2-2222-2-222-2-2-12-12-12-12-111-2-2-1-1-1-1-1-2-222110000-2-200000000111111-1-111002000-2020000-1-10000001100-1-1
χ292222-2-22-2-222222-2-2-2-2222-12-12-12-1-1-2-211-1-1-1-2-2-1-111222200000000-1-1-1-100001111-1-1-200-2200000011000000-1-1001100
χ302222-2-22-2-222222-2-2-2-2222-12-12-12-1-1-2-211-1-1-1-2-2-1-11122-2-200000000111100001111-1-12002-2000000-1-10000001100-1-100
χ312222-2-22-2-222222-2-2-2-222-12-12-12-12-111-2-2-1-1-11122-2-2-1-100002200000000-1-1-1-11111-1-1002000-20-20000-1-1000000110011
χ322222-2-22-2-222222-2-2-2-222-12-12-12-12-111-2-2-1-1-11122-2-2-1-10000-2-20000000011111111-1-100-2000202000011000000-1-100-1-1
χ3322-2-200200002-2-2000000222-2-2-2-2220000-22-2000000002-22i−2i2i−2i2i2i−2i−2i22-2-22i2i−2i−2i000000000000000000000000000000000
χ3422-2-200200002-2-2000000222-2-2-2-2220000-22-2000000002-2−2i2i−2i2i−2i−2i2i2i22-2-2−2i−2i2i2i000000000000000000000000000000000
χ3522-2-200200002-2-2000000222-2-2-2-2220000-22-200000000-222i−2i−2i2i2i2i−2i−2i-2-222−2i−2i2i2i000000000000000000000000000000000
χ3622-2-200200002-2-2000000222-2-2-2-2220000-22-200000000-22−2i2i2i−2i−2i−2i2i2i-2-2222i2i−2i−2i000000000000000000000000000000000
χ372-22-22-222i−2i2i−2i-22-22-22i−2i2i−2i22-2-222-2-222-22-22-2-22i−2i2i−2i2i−2i2i−2i0000000000000000002-22i−2i2i−2i000000000000000000000000000
χ382-22-22-222i−2i2i−2i-22-22-22i−2i2i−2i2-1-212-1-21-12-2-11-1112i−2i−ii−ii2i−2i00000000003−33−30000-11−ii−ii00000000000−i3i3000000−i3i3003−300
χ392-22-22-222i−2i2i−2i-22-22-22i−2i2i−2i2-1-212-1-21-12-2-11-1112i−2i−ii−ii2i−2i0000000000−33−330000-11−ii−ii00000000000i3−i3000000i3−i300−3300
χ402-22-22-222i−2i2i−2i-22-22-22i−2i2i−2i-121-2-121-2-1-112-2-111−ii2i−2i2i−2i−ii000000000000003−33−3-11−ii−ii0000000000000−i3i3000000−i3i3003−3
χ412-22-22-222i−2i2i−2i-22-22-22i−2i2i−2i-121-2-121-2-1-112-2-111−ii2i−2i2i−2i−ii00000000000000−33−33-11−ii−ii0000000000000i3−i3000000i3−i300−33
χ422-22-22-22−2i2i−2i2i-22-22-2−2i2i−2i2i22-2-222-2-222-22-22-2-2−2i2i−2i2i−2i2i−2i2i0000000000000000002-2−2i2i−2i2i000000000000000000000000000
χ432-22-22-22−2i2i−2i2i-22-22-2−2i2i−2i2i2-1-212-1-21-12-2-11-111−2i2ii−ii−i−2i2i00000000003−33−30000-11i−ii−i00000000000i3−i3000000i3−i3003−300
χ442-22-22-22−2i2i−2i2i-22-22-2−2i2i−2i2i2-1-212-1-21-12-2-11-111−2i2ii−ii−i−2i2i0000000000−33−330000-11i−ii−i00000000000−i3i3000000−i3i300−3300
χ452-22-22-22−2i2i−2i2i-22-22-2−2i2i−2i2i-121-2-121-2-1-112-2-111i−i−2i2i−2i2ii−i000000000000003−33−3-11i−ii−i0000000000000i3−i3000000i3−i3003−3
χ462-22-22-22−2i2i−2i2i-22-22-2−2i2i−2i2i-121-2-121-2-1-112-2-111i−i−2i2i−2i2ii−i00000000000000−33−33-11i−ii−i0000000000000−i3i3000000−i3i300−33
χ472-22-2-2222i−2i−2i2i-22-2-222i−2i−2i2i22-2-222-2-22-22-222-2-22i−2i−2i2i2i−2i−2i2i000000000000000000-222i−2i−2i2i000000000000000000000000000
χ482-22-2-2222i−2i−2i2i-22-2-222i−2i−2i2i2-1-212-1-21-1-221-1-1112i−2ii−i−ii−2i2i00000000003−33−300001-1−iii−i00000000000−i3i3000000i3−i300−3300
χ492-22-2-2222i−2i−2i2i-22-2-222i−2i−2i2i2-1-212-1-21-1-221-1-1112i−2ii−i−ii−2i2i0000000000−33−3300001-1−iii−i00000000000i3−i3000000−i3i3003−300
χ502-22-2-2222i−2i−2i2i-22-2-222i−2i−2i2i-121-2-121-2-11-1-22-111−ii−2i2i2i−2ii−i000000000000003−33−31-1−iii−i0000000000000i3−i3000000−i3i300−33
χ512-22-2-2222i−2i−2i2i-22-2-222i−2i−2i2i-121-2-121-2-11-1-22-111−ii−2i2i2i−2ii−i00000000000000−33−331-1−iii−i0000000000000−i3i3000000i3−i3003−3
χ522-22-2-222−2i2i2i−2i-22-2-22−2i2i2i−2i22-2-222-2-22-22-222-2-2−2i2i2i−2i−2i2i2i−2i000000000000000000-22−2i2i2i−2i000000000000000000000000000
χ532-22-2-222−2i2i2i−2i-22-2-22−2i2i2i−2i2-1-212-1-21-1-221-1-111−2i2i−iii−i2i−2i00000000003−33−300001-1i−i−ii00000000000i3−i3000000−i3i300−3300
χ542-22-2-222−2i2i2i−2i-22-2-22−2i2i2i−2i2-1-212-1-21-1-221-1-111−2i2i−iii−i2i−2i0000000000−33−3300001-1i−i−ii00000000000−i3i3000000i3−i3003−300
χ552-22-2-222−2i2i2i−2i-22-2-22−2i2i2i−2i-121-2-121-2-11-1-22-111i−i2i−2i−2i2i−ii000000000000003−33−31-1i−i−ii0000000000000−i3i3000000i3−i300−33
χ562-22-2-222−2i2i2i−2i-22-2-22−2i2i2i−2i-121-2-121-2-11-1-22-111i−i2i−2i−2i2i−ii00000000000000−33−331-1i−i−ii0000000000000i3−i3000000−i3i3003−3
χ5744444444444444444444-2-2-2-2-2-2-2-21-2-2-2-2111-2-2-2-2-2-2-2-2000000000000000000111111000000000000000000000000000
χ584444444-4-4-4-444444-4-4-4-4-2-2-2-2-2-2-2-21-2-2-2-21112222222200000000000000000011-1-1-1-1000000000000000000000000000
χ594444-4-4444-4-4444-4-444-4-4-2-2-2-2-2-2-2-212222111-2-222-2-222000000000000000000-1-111-1-1000000000000000000000000000
χ604444-4-44-4-444444-4-4-4-444-2-2-2-2-2-2-2-21222211122-2-222-2-2000000000000000000-1-1-1-111000000000000000000000000000
χ6144-4-400400004-4-40000004-242-42-4-2-200002-22000000004-400000000-2-2220000000000000000000000000000000000000
χ6244-4-400400004-4-40000004-242-42-4-2-200002-2200000000-440000000022-2-20000000000000000000000000000000000000
χ6344-4-400400004-4-4000000-24-2-42-424-200002-220000000000004i−4i00000000−2i−2i2i2i000000000000000000000000000000000
χ6444-4-400400004-4-4000000-24-2-42-424-200002-22000000000000−4i4i000000002i2i−2i−2i000000000000000000000000000000000
χ654-44-44-444i−4i4i−4i-44-44-44i−4i4i−4i-2-222-2-2221-22-221-1-1−2i2i−2i2i−2i2i−2i2i0000000000000000001-1i−ii−i000000000000000000000000000
χ664-44-44-44−4i4i−4i4i-44-44-4−4i4i−4i4i-2-222-2-2221-22-221-1-12i−2i2i−2i2i−2i2i−2i0000000000000000001-1−ii−ii000000000000000000000000000
χ674-44-4-4444i−4i−4i4i-44-4-444i−4i−4i4i-2-222-2-22212-22-21-1-1−2i2i2i−2i−2i2i2i−2i000000000000000000-11i−i−ii000000000000000000000000000
χ684-44-4-444−4i4i4i−4i-44-4-44−4i4i4i−4i-2-222-2-22212-22-21-1-12i−2i−2i2i2i−2i−2i2i000000000000000000-11−iii−i000000000000000000000000000
χ694-4-440040000-4-4400000044-44-4-44-440000-4-4400000000000000000000000000000000000000000000000000000000000
χ704-4-440040000-4-440000004-2-4-2-4242-2000022-200000000000000000023−23−23230000000000000000000000000000000000000
χ714-4-440040000-4-440000004-2-4-2-4242-2000022-2000000000000000000−232323−230000000000000000000000000000000000000
χ724-4-440040000-4-44000000-24242-4-2-4-2000022-20000000000000000000000−2i32i32i3−2i3000000000000000000000000000000000
χ734-4-440040000-4-44000000-24242-4-2-4-2000022-200000000000000000000002i3−2i3−2i32i3000000000000000000000000000000000
χ74666666-36666-3-3-3-3-3-3-3-3-3000000000000000000000000002200-1-1-1-100000000000000020002020-1-10000-1-1-1-100000000
χ75666666-36666-3-3-3-3-3-3-3-3-300000000000000000000000000-2-2001111000000000000000-2000-20-20110000111100000000
χ76666666-3-6-6-6-6-3-3-3-3-33333000000000000000000000000002200-1-1-1-1000000000000000-2000-202011000011-1-100000000
χ77666666-3-6-6-6-6-3-3-3-3-3333300000000000000000000000000-2-2001111000000000000000200020-20-1-10000-1-11100000000
χ786666-6-6-366-6-6-3-3-333-3-333000000000000000000000000002200-1-1-1-1000000000000000-200020-20110000-1-11100000000
χ796666-6-6-366-6-6-3-3-333-3-33300000000000000000000000000-2-20011110000000000000002000-2020-1-1000011-1-100000000
χ806666-6-6-3-6-666-3-3-33333-3-3000000000000000000000000002200-1-1-1-10000000000000002000-20-20-1-10000111100000000
χ816666-6-6-3-6-666-3-3-33333-3-300000000000000000000000000-2-2001111000000000000000-20002020110000-1-1-1-100000000
χ826-66-66-6-36i−6i6i−6i3-33-33−3i3i−3i3i0000000000000000000000000000003−33−300000000000000000000000−i3i30000−i3i33−300000000
χ836-66-66-6-36i−6i6i−6i3-33-33−3i3i−3i3i000000000000000000000000000000−33−3300000000000000000000000i3−i30000i3−i3−3300000000
χ846-66-66-6-3−6i6i−6i6i3-33-333i−3i3i−3i0000000000000000000000000000003−33−300000000000000000000000i3−i30000i3−i33−300000000
χ856-66-66-6-3−6i6i−6i6i3-33-333i−3i3i−3i000000000000000000000000000000−33−3300000000000000000000000−i3i30000−i3i3−3300000000
χ866-66-6-66-36i−6i−6i6i3-333-3−3i3i3i−3i0000000000000000000000000000003−33−300000000000000000000000i3−i30000−i3i3−3300000000
χ876-66-6-66-36i−6i−6i6i3-333-3−3i3i3i−3i000000000000000000000000000000−33−3300000000000000000000000−i3i30000i3−i33−300000000
χ886-66-6-66-3−6i6i6i−6i3-333-33i−3i−3i3i0000000000000000000000000000003−33−300000000000000000000000−i3i30000i3−i3−3300000000
χ896-66-6-66-3−6i6i6i−6i3-333-33i−3i−3i3i000000000000000000000000000000−33−3300000000000000000000000i3−i30000−i3i33−300000000
χ9088-8-800800008-8-8000000-4-4-44444-420000-22-200000000000000000000000000000000000000000000000000000000000
χ918-8-880080000-8-88000000-4-44-444-4420000-2-2200000000000000000000000000000000000000000000000000000000000
χ921212-12-1200-60000-666000000000000000000000000000000004i−4i00−2i−2i2i2i00000000000000000000000000000000000000000
χ931212-12-1200-60000-66600000000000000000000000000000000−4i4i002i2i−2i−2i00000000000000000000000000000000000000000
χ9412-12-121200-6000066-6000000000000000000000000000000000000−2i32i32i3−2i300000000000000000000000000000000000000000
χ9512-12-121200-6000066-60000000000000000000000000000000000002i3−2i3−2i32i300000000000000000000000000000000000000000

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