Finite Group Databasebeta

← Group #72271846

Character table — Group #72271846

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size1122222224444444444444488888888888888888888888888812121616161616161616161616162424242424242424242424242424243232323232323232324848969696
order122223666222222224444662222444446666666666661212121212124424666612121212121222244444444444444812121212242444448
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ511111111111-1-11111-1-111111-1-1-111-1-1-1111111-1-1-1-1111-1-1-1-111111-1-1111111-1-11-1-11-1-111111-1-1-1-11-1-111-1-1-1-1111-1-1
χ611111111111-1-11111-1-111111-1-1-111-1-1-1111111-1-1-1-1111-1-1-1-1111-1-1-1-1-1-1-1-111-1-11-1-11-1-111111-1-1-1-1-111-1-11111-1-1-111
χ711111111111-1-11111-1-111111-1-1-111-1-1-1111111-1-1-1-1111-1-1-1-11-1-111-1-1111111-1-1-111-111-1-1-1-1-111111-1-111-1-1-1-1-1-1-111
χ811111111111-1-11111-1-111111-1-1-111-1-1-1111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-111-111-1-1-1-1-11111-111-1-11111111-1-1
χ9111111111-1-1111111-1-11111-11-1-1-1-111-111-1-1-1-11111111-1-1-1-111111-1-11111-1-111-11-1-11-1111-1-111-1-1-11-1-1-111-1-111-11-1
χ10111111111-1-1111111-1-11111-11-1-1-1-111-111-1-1-1-11111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-11-1-11-1111-1-111-1-11-1111-1-111-1-11-11
χ11111111111-1-1111111-1-11111-11-1-1-1-111-111-1-1-1-11111111-1-1-1-11-1-111-1-11111-1-1111-111-11-1-1-111-1-111-11-1-1-111-1-1-1-11-11
χ12111111111-1-1111111-1-11111-11-1-1-1-111-111-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111-111-11-1-1-111-1-1111-1111-1-11111-11-1
χ13111111111-1-1-1-11111111111-1-111-1-1-1-1111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-11-1-11111-1-1-1-111-1-11-1-1-1-11111-1-11
χ14111111111-1-1-1-11111111111-1-111-1-1-1-1111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111-11111-1-1-1-111-1
χ15111111111-1-1-1-11111111111-1-111-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-111-111-1-1-1-11111-1-1-1-11-1-1-1-111-1-111-1
χ16111111111-1-1-1-11111111111-1-111-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-111-111-1-1-1-11111-1-111-11111-1-111-1-11
χ172222222220000-2-2-2-222222200-2-200002-2-200000000-2-22222222200-2-2000000000020022-2-20000-2-200000000000000
χ182222222220000-2-2-2-222222200-2-200002-2-200000000-2-2222222-2-200-2-20000000000-200-2-22200002200000000000000
χ192222222220000-2-2-2-2-2-2222200220000-2-2-200000000-2-22-2-2-2-222200220000000000-200-22-2-200002200000000000000
χ202222222220000-2-2-2-2-2-2222200220000-2-2-200000000-2-22-2-2-2-22-2-2002200000000002002-2220000-2-200000000000000
χ2122222222200222-22-200-2-222020000-2-202-2000022222-2-20000-2220000000000-2-20-200-20-22-200220000000000000000
χ2222222222200222-22-200-2-222020000-2-202-2000022222-2-20000-2-2-20000000000-2-20200202-2200-2-20000000000000000
χ2322222222200-2-22-22-200-2-2220-200002202-20000-2-2-2-22-2-20000-222000000000022020020-22-200-2-20000000000000000
χ2422222222200-2-22-22-200-2-2220-200002202-20000-2-2-2-22-2-20000-2-2-20000000000220-200-202-2200220000000000000000
χ252222222222200-22-2200-2-2222000-2-2000-2222220000-22-20000-22200000000-2-200-200-200-2-2222000000000000000000
χ262222222222200-22-2200-2-2222000-2-2000-2222220000-22-20000-2-2-200000000-2-20020020022-2-2-2000000000000000000
χ27222222222-2-200-22-2200-2-222-200022000-22-2-2-2-20000-22-20000-222000000002200200200-2-22-2-2000000000000000000
χ28222222222-2-200-22-2200-2-222-200022000-22-2-2-2-20000-22-20000-2-2-2000000002200-200-20022-222000000000000000000
χ2922222-1-1-1-1222222222222-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10022-1-1-1-1-1-1-1-1-1-1000000000000000222-1-1-1-1-1-100000
χ3022222-1-1-1-1222222222222-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-1-11111-1-1-1-1000000000000000-2-2-211111100000
χ3122222-1-1-1-122-2-22222-2-222-1-12-2-2-222-2-2-2-1-1-1-1-1-11111-1-1-11111-1002211-1-1-1-1-1-1110000000000000002-2-2-1-1111100000
χ3222222-1-1-1-122-2-22222-2-222-1-12-2-2-222-2-2-2-1-1-1-1-1-11111-1-1-11111-100-2-2111111-1-111000000000000000-22211-1-1-1-100000
χ3322222-1-1-1-1-2-2222222-2-222-1-1-22-2-2-2-222-2-1-11111-1-1-1-1-1-1-11111-1002211-1-1-1-111-1-1000000000000000-22-211-1-11100000
χ3422222-1-1-1-1-2-2222222-2-222-1-1-22-2-2-2-222-2-1-11111-1-1-1-1-1-1-11111-100-2-211111111-1-10000000000000002-22-1-111-1-100000
χ3522222-1-1-1-1-2-2-2-222222222-1-1-2-222-2-2-2-22-1-111111111-1-1-1-1-1-1-1-10022-1-1-1-1-1-11111000000000000000-2-221111-1-100000
χ3622222-1-1-1-1-2-2-2-222222222-1-1-2-222-2-2-2-22-1-111111111-1-1-1-1-1-1-1-100-2-2-1-11111111100000000000000022-2-1-1-1-11100000
χ3722-2-222-2-220000-2-222222-2-22002-20000-22200000000-2-2-222-2-2200002-200000000220-2-200002-22-20000000000000000
χ3822-2-222-2-220000-2-222222-2-22002-20000-22200000000-2-2-222-2-2200002-200000000-2-20220000-22-220000000000000000
χ3922-2-222-2-220000-2-222-2-22-2-2200-22000022200000000-2-2-2-2-22220000-22000000002-20-2200002-2-220000000000000000
χ4022-2-222-2-220000-2-222-2-22-2-2200-22000022200000000-2-2-2-2-22220000-2200000000-2202-20000-222-20000000000000000
χ4122-2-222-2-2200222-2-2200-22-220-200002-20-22000022-2-22-220000-20000000000002-2202-20-2000-22002-200000000000000
χ4222-2-222-2-2200222-2-2200-22-220-200002-20-22000022-2-22-220000-20000000000002-2-20-22020002-200-2200000000000000
χ4322-2-222-2-2200-2-22-2-2200-22-22020000-220-220000-2-2222-220000-2000000000000-2220-2-202000-2200-2200000000000000
χ4422-2-222-2-2200-2-22-2-2200-22-22020000-220-220000-2-2222-220000-2000000000000-22-20220-20002-2002-200000000000000
χ4522-2-222-2-222200-222-200-22-22-20002-20002-222-2-20000-2220000-200000000002-2000220-2-200000-22-2200000000000000
χ4622-2-222-2-222200-222-200-22-22-20002-20002-222-2-20000-2220000-200000000002-2000-2-2022000002-22-200000000000000
χ4722-2-222-2-22222222-2-2222-2-22-2-2-22-22-22-2-2-222-2-222-2-222-222-2-220000-220000-22-2200000000000000000000000000000
χ4822-2-222-2-2222-2-222-2-2-2-22-2-22-222-2-222-22-2-222-2-2-2-22222-2-2-222200002-20000-222-200000000000000000000000000000
χ4922-2-222-2-22-2-200-222-200-22-222000-220002-2-2-2220000-2220000-20000000000-220002-20-2200000-222-200000000000000
χ5022-2-222-2-22-2-200-222-200-22-222000-220002-2-2-2220000-2220000-20000000000-22000-2202-2000002-2-2200000000000000
χ5122-2-222-2-22-2-22222-2-2-2-22-2-222-22-22-2-222-2-2-2-22222-2-222-2-2-222200002-200002-2-2200000000000000000000000000000
χ5222-2-222-2-22-2-2-2-222-2-2222-2-2222-222-22-2-2-2-2-2-222-2-22222-222-2-220000-2200002-22-200000000000000000000000000000
χ5322-2-22-111-1222222-2-2222-21-1-2-2-22-22-22-211-1-111-1-111-1-11-1-111-100001-1−i3i3−i3i31-11-1000000000000000000−i3i3−i3i3−i3i300000
χ5422-2-22-111-1222222-2-2222-21-1-2-2-22-22-22-211-1-111-1-111-1-11-1-111-100001-1i3−i3i3−i31-11-1000000000000000000i3−i3i3−i3i3−i300000
χ5522-2-22-111-122-2-222-2-2-2-22-21-1-222-2-222-2211-1-11111-1-1-1-1111-1-1-10000-11−i3i3−i3i31-1-11000000000000000000−i3i3i3−i3i3−i300000
χ5622-2-22-111-122-2-222-2-2-2-22-21-1-222-2-222-2211-1-11111-1-1-1-1111-1-1-10000-11i3−i3i3−i31-1-11000000000000000000i3−i3−i3i3−i3i300000
χ5722-2-22-111-1-2-22222-2-2-2-22-21-12-22-22-2-2221111-1-1-1-111-1-1111-1-1-10000-11−i3i3−i3i3-111-1000000000000000000i3−i3−i3i3i3−i300000
χ5822-2-22-111-1-2-22222-2-2-2-22-21-12-22-22-2-2221111-1-1-1-111-1-1111-1-1-10000-11i3−i3i3−i3-111-1000000000000000000−i3i3i3−i3−i3i300000
χ5922-2-22-111-1-2-2-2-222-2-2222-21-122-222-22-2-21111-1-111-1-1-1-11-1-111-100001-1−i3i3−i3i3-11-11000000000000000000i3−i3i3−i3−i3i300000
χ6022-2-22-111-1-2-2-2-222-2-2222-21-122-222-22-2-21111-1-111-1-1-1-11-1-111-100001-1i3−i3i3−i3-11-11000000000000000000−i3i3−i3i3i3−i300000
χ6144444-2-2-2-20000-4-4-4-44444-2-200-4-400004220000000022-2-2-2-2-2-20000220000000000000000000000000000000000000
χ6244444-2-2-2-20000-4-4-4-4-4-444-2-200440000-4220000000022-22222-20000-2-20000000000000000000000000000000000000
χ6344444-2-2-2-200444-44-400-4-4-2-2040000-4-40-220000-2-2-2-2-222000020000000000002200000000000000000000000000000
χ6444444-2-2-2-200-4-44-44-400-4-4-2-20-40000440-2200002222-22200002000000000000-2-200000000000000000000000000000
χ6544444-2-2-2-24400-44-4400-4-4-2-24000-4-40002-2-2-2-2-200002-22000020000000000220000000000000000000000000000000
χ6644444-2-2-2-2-4-400-44-4400-4-4-2-2-4000440002-2222200002-22000020000000000-2-20000000000000000000000000000000
χ67444-4-44444000000000000-4-40000000000000000000000000004i−4i2-20022-2-200000000000000000000000000002i−2i000
χ68444-4-44444000000000000-4-40000000000000000000000000004i−4i-2200-2-2220000000000000000000000000000−2i2i000
χ69444-4-44444000000000000-4-4000000000000000000000000000−4i4i2-20022-2-20000000000000000000000000000−2i2i000
χ70444-4-44444000000000000-4-4000000000000000000000000000−4i4i-2200-2-22200000000000000000000000000002i−2i000
χ7144-4-44-222-20000-4-444444-42-2004-40000-4-2-200000000222-2-222-20000-220000000000000000000000000000000000000
χ7244-4-44-222-20000-4-444-4-44-42-200-4400004-2-20000000022222-2-2-200002-20000000000000000000000000000000000000
χ7344-4-44-222-200444-4-4400-442-20-400004-402-20000-2-222-22-200002000000000000-2200000000000000000000000000000
χ7444-4-44-222-200-4-44-4-4400-442-2040000-4402-2000022-2-2-22-2000020000000000002-200000000000000000000000000000
χ7544-4-44-222-24400-444-400-442-2-40004-4000-22-2-22200002-2-2000020000000000-220000000000000000000000000000000
χ7644-4-44-222-2-4-400-444-400-442-24000-44000-2222-2-200002-2-20000200000000002-20000000000000000000000000000000
χ77888-8-8-4-4-4-400000000000044000000000000000000000000000004-400-2-222000000000000000000000000000000000
χ78888-8-8-4-4-4-40000000000004400000000000000000000000000000-440022-2-2000000000000000000000000000000000
χ7988-88-88-8-880000000000008-80000000000000000000000000000000000000000000000000000000000000000000000
χ8088-88-8-444-4000000000000-44000000000000000000000000000000000−2i32i32i3−2i3000000000000000000000000000000000
χ8188-88-8-444-4000000000000-440000000000000000000000000000000002i3−2i3−2i32i3000000000000000000000000000000000
χ828-8000800-84-44-400004-40000000000000004-4004-4000004-40000000000000000000000000000000000000000000000
χ838-8000800-84-4-440000-440000000000000004-400-4400000-440000000000000000000000000000000000000000000000
χ848-8000800-8-444-40000-44000000000000000-44004-400000-440000000000000000000000000000000000000000000000
χ858-8000800-8-44-4400004-4000000000000000-4400-44000004-40000000000000000000000000000000000000000000000
χ868-8000-4−4i34i344-44-400004-4000000000000000-22−2i32i3-22−2i32i3000-22−2i32i300000000000000000000000000000000000000000000
χ878-8000-4−4i34i344-4-440000-44000000000000000-22−2i32i32-22i3−2i30002-22i3−2i300000000000000000000000000000000000000000000
χ888-8000-4−4i34i34-444-40000-440000000000000002-22i3−2i3-22−2i32i30002-22i3−2i300000000000000000000000000000000000000000000
χ898-8000-4−4i34i34-44-4400004-40000000000000002-22i3−2i32-22i3−2i3000-22−2i32i300000000000000000000000000000000000000000000
χ908-8000-44i3−4i344-44-400004-4000000000000000-222i3−2i3-222i3−2i3000-222i3−2i300000000000000000000000000000000000000000000
χ918-8000-44i3−4i344-4-440000-44000000000000000-222i3−2i32-2−2i32i30002-2−2i32i300000000000000000000000000000000000000000000
χ928-8000-44i3−4i34-444-40000-440000000000000002-2−2i32i3-222i3−2i30002-2−2i32i300000000000000000000000000000000000000000000
χ938-8000-44i3−4i34-44-4400004-40000000000000002-2−2i32i32-2−2i32i3000-222i3−2i300000000000000000000000000000000000000000000

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