Finite Group Databasebeta

← Group #72272021

Character table — Group #72272021

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size1122222444444444444444448888888888888888888812121212161616161616161616161616161616161616161616242424242424242424242424242432323232323296969696
order12222362222224444666666622224444446666661212121244442444666661212121212121212121212122222224444444444121212124488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1111-1-111-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111-1-111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111-1-111-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-111
χ91111111-1-11111-1-1111111111-1-11-11-111-1-111-1-1-1-111-1-111-1-111-1-1-11-1111-11111-1-1-1-1-1-111-1-11-11-11-111-1-11-111-1-11-11-1
χ101111111-1-11111-1-1111111111-1-11-11-111-1-111-1-1-1-111-1-111-1-1-1-111-11-1-1-11-1-1-111-1-1111111-1-11-11-11-111-1-1-11-1-111-11-11
χ111111111-1-11111-1-1111111111-1-11-11-111-1-111-1-1-1-111-1-1-1-11111-1-1-11-1111-11111-1-1-1-1-1-1-1-111-11-11-11-1-1111-111-1-1-11-11
χ121111111-1-11111-1-1111111111-1-11-11-111-1-111-1-1-1-111-1-1-1-111-1-111-11-1-1-11-1-1-111-1-11111-1-111-11-11-11-1-111-11-1-1111-11-1
χ131111111-1-11111-1-1111111111-1-1-11-11-1-11111-1-1-1-111-1-111-1-111-1-1-1-1111-1111-1-111-1-1-1-111-1-1-11-111-1-1-111-11-1-111-111-1
χ141111111-1-11111-1-1111111111-1-1-11-11-1-11111-1-1-1-111-1-111-1-1-1-111-1-11-1-1-11-1-1-1-111111111-1-1-11-111-1-1-1111-111-1-11-1-11
χ151111111-1-11111-1-1111111111-1-1-11-11-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1111-1111-1-111-1-1-1-1-1-1111-11-1-1111-1-1-11-1-1111-1-11
χ161111111-1-11111-1-1111111111-1-1-11-11-1-11111-1-1-1-111-1-1-1-111-1-111-1-11-1-1-11-1-1-1-1111111-1-1111-11-1-1111-1-11-111-1-1-111-1
χ1722222222222-2-2-2-2-2-222222222-22-22-2-2-222-2-222-2-2-2-2-2-20000000022-2002-200-2-2220000000000000000000000000000
χ1822222222222-2-2-2-2-2-222222222-2-22-2222-2-2-2-222-2-2-2-2-2-2000000002-2200-220022-2-20000000000000000000000000000
χ19222222222-2-222-2-2-2-22-2-2-2-222-2200000000222222-2-2-2-200000000-2000000000000000000002-22-200-2-2220000000000
χ20222222222-2-222-2-2-2-22-2-2-2-222-2200000000222222-2-2-2-200000000-200000000000000000000-22-220022-2-20000000000
χ21222222222-2-2-2-222222-2-2-2-222-2-200000000-2-222-2-2222222220000-20000000000000000-2-2-2-200002200000000000000
χ22222222222-2-2-2-222222-2-2-2-222-2-200000000-2-222-2-22222-2-2-2-20000-2000000000000000022220000-2-200000000000000
χ232222222-2-222-2-222-2-22222222-222222-2-2-2-2-2-2-2-222-2-22200000000-222002200-2-2-2-20000000000000000000000000000
χ242222222-2-222-2-222-2-22222222-22-2-2-2-22222-2-2-2-222-2-22200000000-2-2-200-2-20022220000000000000000000000000000
χ252222222-2-2-2-22222-2-22-2-2-2-2222-20000000022-2-2-2-2-2-22200000000200000000000000000000222200-2-2-2-20000000000
χ262222222-2-2-2-22222-2-22-2-2-2-2222-20000000022-2-2-2-2-2-22200000000200000000000000000000-2-2-2-20022220000000000
χ272222222-2-2-2-2-2-2-2-2222-2-2-2-2222200000000-2-2-2-22222-2-222-2-2000020000000000000000-2-22200002-200000000000000
χ282222222-2-2-2-2-2-2-2-2222-2-2-2-2222200000000-2-2-2-22222-2-2-2-22200002000000000000000022-2-20000-2200000000000000
χ2922222-1-12222222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-100002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000022-1-1-1-10000
χ3022222-1-12222222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-10000-2-2-2-2-1-1-111-1-111-1-1-1-1111100000000000000-2-211110000
χ3122222-1-12222222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-100002222-111-1-111-1-11111-1-1-1-100000000000000-2-211110000
χ3222222-1-12222222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-10000-2-2-2-2-111111111111111110000000000000022-1-1-1-10000
χ3322222-1-12222-2-2-2-2-2-2-1-1-1-1-1-1-12-22-22-2-2-22211-1-111111100000000-1-11i3−i3-11i3−i311-1-1i3i3−i3−i30000000000000000i3−i3i3−i30000
χ3422222-1-12222-2-2-2-2-2-2-1-1-1-1-1-1-12-22-22-2-2-22211-1-111111100000000-1-11−i3i3-11−i3i311-1-1−i3−i3i3i30000000000000000−i3i3−i3i30000
χ3522222-1-12222-2-2-2-2-2-2-1-1-1-1-1-1-12-2-22-2222-2-211-1-111111100000000-11-1i3−i31-1i3−i3-1-111i3i3−i3−i30000000000000000−i3i3−i3i30000
χ3622222-1-12222-2-2-2-2-2-2-1-1-1-1-1-1-12-2-22-2222-2-211-1-111111100000000-11-1−i3i31-1−i3i3-1-111−i3−i3i3i30000000000000000i3−i3i3−i30000
χ3722222-1-1-2-22222-2-222-1-1-1-1-1-1-1-2-22-22-222-2-2-1-11111-1-111000022-2-21-11-1-1-11-1-1-1-1111111000000000000002-2-1-1110000
χ3822222-1-1-2-22222-2-222-1-1-1-1-1-1-1-2-22-22-222-2-2-1-11111-1-1110000-2-2221-1111-1111-1-111-1-1-1-100000000000000-2211-1-10000
χ3922222-1-1-2-22222-2-222-1-1-1-1-1-1-1-2-2-22-22-2-222-1-11111-1-111000022-2-211-1-1-11-1-1-111-1-1111100000000000000-2211-1-10000
χ4022222-1-1-2-22222-2-222-1-1-1-1-1-1-1-2-2-22-22-2-222-1-11111-1-1110000-2-22211-1111-11111-1-1-1-1-1-1000000000000002-2-1-1110000
χ4122222-1-1-2-222-2-222-2-2-1-1-1-1-1-1-1-222222-2-2-2-21111-1-111-1-1000000001-1-1i3−i3-1-1i3−i31111−i3−i3i3i30000000000000000i3−i3−i3i30000
χ4222222-1-1-2-222-2-222-2-2-1-1-1-1-1-1-1-222222-2-2-2-21111-1-111-1-1000000001-1-1−i3i3-1-1−i3i31111i3i3−i3−i30000000000000000−i3i3i3−i30000
χ4322222-1-1-2-222-2-222-2-2-1-1-1-1-1-1-1-22-2-2-2-222221111-1-111-1-100000000111i3−i311i3−i3-1-1-1-1−i3−i3i3i30000000000000000−i3i3i3−i30000
χ4422222-1-1-2-222-2-222-2-2-1-1-1-1-1-1-1-22-2-2-2-222221111-1-111-1-100000000111−i3i311−i3i3-1-1-1-1i3i3−i3−i30000000000000000i3−i3−i3i30000
χ4522-2-2222002-22-2002-2-222-2-22-200020-2002-22-200002-20000220000002000-200002-20000002-220-200-22-2000000000000
χ4622-2-2222002-22-2002-2-222-2-22-200020-2002-22-200002-20000-2-20000002000-200002-2000000-22-202002-22000000000000
χ4722-2-2222002-22-2002-2-222-2-22-2000-20200-222-200002-2000022000000-200020000-220000002-2-20200-2-22000000000000
χ4822-2-2222002-22-2002-2-222-2-22-2000-20200-222-200002-20000-2-2000000-200020000-22000000-2220-20022-2000000000000
χ4922-2-2222002-2-2200-22-222-2-22-200020-200-22-220000-220022000000002000-20000-2200002-200020-2-20002-20000000000
χ5022-2-2222002-2-2200-22-222-2-22-200020-200-22-220000-2200-2-2000000002000-20000-220000-22000-2022000-220000000000
χ5122-2-2222002-2-2200-22-222-2-22-2000-202002-2-220000-22002200000000-2000200002-200002-2000-202-2000-220000000000
χ5222-2-2222002-2-2200-22-222-2-22-2000-202002-2-220000-2200-2-200000000-2000200002-20000-2200020-220002-20000000000
χ5322-2-222200-222-200-22-2-2-2222-20020-202-2002-20000-22002200000002000-20002-2000000-220020-20-20-22000000000000
χ5422-2-222200-222-200-22-2-2-2222-20020-202-2002-20000-2200-2-200000002000-20002-20000002-200-2020202-2000000000000
χ5522-2-222200-222-200-22-2-2-2222-200-2020-22002-20000-2200220000000-20002000-22000000-2200-2020-202-2000000000000
χ5622-2-222200-222-200-22-2-2-2222-200-2020-22002-20000-2200-2-20000000-20002000-220000002-20020-2020-22000000000000
χ5722-2-222200-22-22002-2-2-2-2222-20020-20-2200-2200002-2000022000002000-2000-2200000000-22020-20-200-220000000000
χ5822-2-222200-22-22002-2-2-2-2222-20020-20-2200-2200002-20000-2-2000002000-2000-22000000002-20-20202002-20000000000
χ5922-2-222200-22-22002-2-2-2-2222-200-20202-200-2200002-200002200000-200020002-200000000-220-2020-2002-20000000000
χ6022-2-222200-22-22002-2-2-2-2222-200-20202-200-2200002-20000-2-200000-200020002-2000000002-2020-20200-220000000000
χ6144444-2-244-4-444-4-4-4-4-22222-2-2-4400000000-2-2-2-2-2-222220000000020000000000000000000000000000000000000000
χ6244444-2-244-4-4-4-44444-22222-2-2-4-40000000022-2-222-2-2-2-20000000020000000000000000000000000000000000000000
χ6344444-2-2-4-4-4-44444-4-4-22222-2-24-400000000-2-2222222-2-200000000-20000000000000000000000000000000000000000
χ6444444-2-2-4-4-4-4-4-4-4-444-22222-2-244000000002222-2-2-2-22200000000-20000000000000000000000000000000000000000
χ6544-44-4440000004-400-40000-440000000000000000004-400002-22-20002200-2-200002-22-2000000000000000000000000
χ6644-44-4440000004-400-40000-440000000000000000004-40000-22-22000-2-200220000-22-22000000000000000000000000
χ6744-44-444000000-4400-40000-44000000000000000000-4400002-2-220002200-2-20000-22-22000000000000000000000000
χ6844-44-444000000-4400-40000-44000000000000000000-440000-222-2000-2-2002200002-22-2000000000000000000000000
χ6944-44-4-2-20000004-40022i3−2i32i3−2i32-2000000000000002i3−2i300-2200002-22-2000−1+i3−1−i3001−i31+i30000−1−i31+i3−1+i31−i3000000000000000000000000
χ7044-44-4-2-20000004-40022i3−2i32i3−2i32-2000000000000002i3−2i300-220000-22-220001−i31+i300−1+i3−1−i300001+i3−1−i31−i3−1+i3000000000000000000000000
χ7144-44-4-2-20000004-4002−2i32i3−2i32i32-200000000000000−2i32i300-2200002-22-2000−1−i3−1+i3001+i31−i30000−1+i31−i3−1−i31+i3000000000000000000000000
χ7244-44-4-2-20000004-4002−2i32i3−2i32i32-200000000000000−2i32i300-220000-22-220001+i31−i300−1−i3−1+i300001−i3−1+i31+i3−1−i3000000000000000000000000
χ7344-44-4-2-2000000-440022i3−2i32i3−2i32-200000000000000−2i32i3002-200002-2-22000−1+i3−1−i3001−i31+i300001+i3−1−i31−i3−1+i3000000000000000000000000
χ7444-44-4-2-2000000-440022i3−2i32i3−2i32-200000000000000−2i32i3002-20000-222-20001−i31+i300−1+i3−1−i30000−1−i31+i3−1+i31−i3000000000000000000000000
χ7544-44-4-2-2000000-44002−2i32i3−2i32i32-2000000000000002i3−2i3002-200002-2-22000−1−i3−1+i3001+i31−i300001−i3−1+i31+i3−1−i3000000000000000000000000
χ7644-44-4-2-2000000-44002−2i32i3−2i32i32-2000000000000002i3−2i3002-20000-222-20001+i31−i300−1−i3−1+i30000−1+i31−i3−1−i31+i3000000000000000000000000
χ7744-4-44-2-2004-44-4004-42-2-222-2200040-4004-4-220000-22000000000000-200020000-220000000000000000000000000000
χ7844-4-44-2-2004-44-4004-42-2-222-22000-40400-44-220000-220000000000002000-200002-20000000000000000000000000000
χ7944-4-44-2-2004-4-4400-442-2-222-2200040-400-442-200002-2000000000000-2000200002-20000000000000000000000000000
χ8044-4-44-2-2004-4-4400-442-2-222-22000-404004-42-200002-20000000000002000-20000-220000000000000000000000000000
χ8144-4-44-2-200-444-400-44222-2-2-220040-404-400-2200002-200000000000-20002000-22000000000000000000000000000000
χ8244-4-44-2-200-444-400-44222-2-2-2200-4040-4400-2200002-2000000000002000-20002-2000000000000000000000000000000
χ8344-4-44-2-200-44-44004-4222-2-2-220040-40-44002-20000-2200000000000-200020002-2000000000000000000000000000000
χ8444-4-44-2-200-44-44004-4222-2-2-2200-40404-4002-20000-22000000000002000-2000-22000000000000000000000000000000
χ85888-8-888000000000080000-8-8000000000000000000000000000000000000000000000000000000000000000000000
χ86888-8-8-4-40000000000-44i3−4i3−4i34i344000000000000000000000000000000000000000000000000000000000000000000000
χ87888-8-8-4-40000000000-4−4i34i34i3−4i344000000000000000000000000000000000000000000000000000000000000000000000
χ888-80008-84-40000000000000000000000000004-40000004-44-4000000000000000000000000000000000000000000000
χ898-80008-84-40000000000000000000000000004-4000000-44-44000000000000000000000000000000000000000000000
χ908-80008-8-44000000000000000000000000000-440000004-4-44000000000000000000000000000000000000000000000
χ918-80008-8-44000000000000000000000000000-44000000-444-4000000000000000000000000000000000000000000000
χ9216-16000-888-8000000000000000000000000000-440000000000000000000000000000000000000000000000000000000
χ9316-16000-88-880000000000000000000000000004-40000000000000000000000000000000000000000000000000000000

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