Finite Group Databasebeta

← Group #72277119

Character table — Group #72277119

Order 8064.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73
size116667777121212122428282828282832323636364242487272728484848484848484848484848484144144144168168168168168168168168192192224224224224224224224224224224336336336336336
order122714336624442226666361428286681428282266666612121212121214565644661212121221423366666666412122424
χ11111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111-1-1-1-1-1-111111111111-1-1-1-1-1-111111111111-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-111
χ31111111111-1-11-11111111111111-11-1-1-1-1-1-1-1-111-1-1-1-111-1-1-11-1-1-111-1-1111111111111-1-1-1-1-1
χ41111111111-1-11-1-1-1-1-1-1-11111111-11-1-111111111-1-1-1-111-1-1-1-11-1-1-1-1111111-1-111-1-1-1-1111-1-1
χ511111−1+i32−1−i32−1+i32−1−i321111111−1+i32−1+i32−1−i32−1−i3211111−1+i32−1−i32111111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i32
χ611111−1+i32−1−i32−1+i32−1−i3211111-1-11−i321−i321+i321+i3211111−1+i32−1−i321111-1-11−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111-1-1−1+i32−1−i321−i321+i321−i321+i3211−1+i32−1−i32-1-1−1+i32−1−i321−i321−i321+i321+i32-11−i321+i32−1+i32−1−i32
χ711111−1+i32−1−i32−1+i32−1−i321-1-11-111−1+i32−1+i32−1−i32−1−i3211111−1+i32−1−i32-11-1-1-1-11−i321−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32-1-1-11-11−i321+i32−1+i32−1−i321−i321+i3211−1+i32−1−i3211−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32-11−i321+i321−i321+i32
χ811111−1+i32−1−i32−1+i32−1−i321-1-11-1-1-11−i321−i321+i321+i3211111−1+i32−1−i32-11-1-111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32-1-1-1-111−i321+i321−i321+i32−1+i32−1−i3211−1+i32−1−i32-1-1−1+i32−1−i321−i321−i321+i321+i321−1+i32−1−i321−i321+i32
χ911111−1−i32−1+i32−1−i32−1+i321111111−1−i32−1−i32−1+i32−1+i3211111−1−i32−1+i32111111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i32
χ1011111−1−i32−1+i32−1−i32−1+i3211111-1-11+i321+i321−i321−i3211111−1−i32−1+i321111-1-11+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111-1-1−1−i32−1+i321+i321−i321+i321−i3211−1−i32−1+i32-1-1−1−i32−1+i321+i321+i321−i321−i32-11+i321−i32−1−i32−1+i32
χ1111111−1−i32−1+i32−1−i32−1+i321-1-11-111−1−i32−1−i32−1+i32−1+i3211111−1−i32−1+i32-11-1-1-1-11+i321+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32-1-1-11-11+i321−i32−1−i32−1+i321+i321−i3211−1−i32−1+i3211−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32-11+i321−i321+i321−i32
χ1211111−1−i32−1+i32−1−i32−1+i321-1-11-1-1-11+i321+i321−i321−i3211111−1−i32−1+i32-11-1-111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32-1-1-1-111+i321−i321+i321−i32−1−i32−1+i3211−1−i32−1+i32-1-1−1−i32−1+i321+i321+i321−i321−i321−1−i32−1+i321+i321−i32
χ1322222222220020222222-1-12222202000000002200002200020002200-1-1-1-1-1-1-1-1-1-1-1-100000
χ1422222222220020-2-2-2-2-2-2-1-122222020000000022000022000-2000-2-200-1-1-1-111-1-1111100000
χ1522222−1+i3−1−i3−1+i3−1−i32002022−1+i3−1+i3−1−i3−1−i3-1-1222−1+i3−1−i30200000000−1+i3−1−i30000−1+i3−1−i30002000−1+i3−1−i300-1-11−i321+i32-1-11−i321+i321−i321−i321+i321+i3200000
χ1622222−1+i3−1−i3−1+i3−1−i320020-2-21−i31−i31+i31+i3-1-1222−1+i3−1−i30200000000−1+i3−1−i30000−1+i3−1−i3000-20001−i31+i300-1-11−i321+i32111−i321+i32−1+i32−1+i32−1−i32−1−i3200000
χ1722222−1−i3−1+i3−1−i3−1+i32002022−1−i3−1−i3−1+i3−1+i3-1-1222−1−i3−1+i30200000000−1−i3−1+i30000−1−i3−1+i30002000−1−i3−1+i300-1-11+i321−i32-1-11+i321−i321+i321+i321−i321−i3200000
χ1822222−1−i3−1+i3−1−i3−1+i320020-2-21+i31+i31−i31−i3-1-1222−1−i3−1+i30200000000−1−i3−1+i30000−1−i3−1+i3000-20001+i31−i300-1-11+i321−i32111+i321−i32−1−i32−1−i32−1+i32−1+i3200000
χ19333333333-111-11333333003-1-133-1-111111111-1-11111-1-11-1-1-1111-1-111000000000000-1-1-1-1-1
χ20333333333-111-11-3-3-3-3-3-3003-1-133-1-111-1-1-1-1-1-1-1-11111-1-11-1-11-11111-1-1000000000000111-1-1
χ21333333333-1-1-1-1-1333333003-1-1331-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-100000000000011111
χ22333333333-1-1-1-1-1-3-3-3-3-3-3003-1-1331-1-1-1111111-1-1-1-1-1-1-1-1-11111-1-11111000000000000-1-1-111
χ2333333−3+3i32−3−3i32−3+3i32−3−3i32-111-1133−3+3i32−3+3i32−3−3i32−3−3i32003-1-1−3+3i32−3−3i32-1-11111−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i321-1-1-11−1+i32−1−i321−i321+i32−1+i32−1−i32000000000000-11−i321+i321−i321+i32
χ2433333−3+3i32−3−3i32−3+3i32−3−3i32-111-11-3-33−3i323−3i323+3i323+3i32003-1-1−3+3i32−3−3i32-1-111-1-11−i321−i321+i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i321-1-11-1−1+i32−1−i32−1+i32−1−i321−i321+i320000000000001−1+i32−1−i321−i321+i32
χ2533333−3+3i32−3−3i32−3+3i32−3−3i32-1-1-1-1-133−3+3i32−3+3i32−3−3i32−3−3i32003-1-1−3+3i32−3−3i321-1-1-1-1-11−i321−i321+i321+i321−i321+i321−i321−i321+i321+i321−i321+i32-111-1-11−i321+i321−i321+i321−i321+i320000000000001−1+i32−1−i32−1+i32−1−i32
χ2633333−3+3i32−3−3i32−3+3i32−3−3i32-1-1-1-1-1-3-33−3i323−3i323+3i323+3i32003-1-1−3+3i32−3−3i321-1-1-111−1+i32−1+i32−1−i32−1−i321−i321+i321−i321−i321+i321+i321−i321+i32-111111−i321+i32−1+i32−1−i32−1+i32−1−i32000000000000-11−i321+i32−1+i32−1−i32
χ2733333−3−3i32−3+3i32−3−3i32−3+3i32-111-1133−3−3i32−3−3i32−3+3i32−3+3i32003-1-1−3−3i32−3+3i32-1-11111−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i321-1-1-11−1−i32−1+i321+i321−i32−1−i32−1+i32000000000000-11+i321−i321+i321−i32
χ2833333−3−3i32−3+3i32−3−3i32−3+3i32-111-11-3-33+3i323+3i323−3i323−3i32003-1-1−3−3i32−3+3i32-1-111-1-11+i321+i321−i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i321-1-11-1−1−i32−1+i32−1−i32−1+i321+i321−i320000000000001−1−i32−1+i321+i321−i32
χ2933333−3−3i32−3+3i32−3−3i32−3+3i32-1-1-1-1-133−3−3i32−3−3i32−3+3i32−3+3i32003-1-1−3−3i32−3+3i321-1-1-1-1-11+i321+i321−i321−i321+i321−i321+i321+i321−i321−i321+i321−i32-111-1-11+i321−i321+i321−i321+i321−i320000000000001−1−i32−1+i32−1−i32−1+i32
χ3033333−3−3i32−3+3i32−3−3i32−3+3i32-1-1-1-1-1-3-33+3i323+3i323−3i323−3i32003-1-1−3−3i32−3+3i321-1-1-111−1−i32−1−i32−1+i32−1+i321+i321−i321+i321+i321−i321−i321+i321−i32-111111+i321−i32−1−i32−1+i32−1−i32−1+i32000000000000-11+i321−i32−1−i32−1+i32
χ314-404-444-4-402-2002-22-22-21-100000002-22-22-22-2002-22-200000000000001-1111-1-1-11-11-100000
χ324-404-444-4-402-200-22-22-221-100000002-2-22-22-22002-22-200000000000001-111-11-1-1-11-1100000
χ334-404-444-4-40-22002-22-22-21-10000000-22-22-22-2200-22-2200000000000001-1111-1-1-11-11-100000
χ344-404-444-4-40-2200-22-22-221-10000000-222-22-22-200-22-2200000000000001-111-11-1-1-11-1100000
χ354-404-4−2+2i3−2−2i32−2i32+2i302-2002-2−1+i31−i3−1−i31+i31-100000002-22-2−1+i31−i3−1−i31+i300−1+i31−i3−1−i31+i300000000000001-1−1+i32−1−i321-11−i321+i32−1+i321−i32−1−i321+i3200000
χ364-404-4−2+2i3−2−2i32−2i32+2i302-200-221−i3−1+i31+i3−1−i31-100000002-2-221−i3−1+i31+i3−1−i300−1+i31−i3−1−i31+i300000000000001-1−1+i32−1−i32-111−i321+i321−i32−1+i321+i32−1−i3200000
χ374-404-4−2+2i3−2−2i32−2i32+2i30-22002-2−1+i31−i3−1−i31+i31-10000000-22-221−i3−1+i31+i3−1−i3001−i3−1+i31+i3−1−i300000000000001-1−1+i32−1−i321-11−i321+i32−1+i321−i32−1−i321+i3200000
χ384-404-4−2+2i3−2−2i32−2i32+2i30-2200-221−i3−1+i31+i3−1−i31-10000000-222-2−1+i31−i3−1−i31+i3001−i3−1+i31+i3−1−i300000000000001-1−1+i32−1−i32-111−i321+i321−i32−1+i321+i32−1−i3200000
χ394-404-4−2−2i3−2+2i32+2i32−2i302-2002-2−1−i31+i3−1+i31−i31-100000002-22-2−1−i31+i3−1+i31−i300−1−i31+i3−1+i31−i300000000000001-1−1−i32−1+i321-11+i321−i32−1−i321+i32−1+i321−i3200000
χ404-404-4−2−2i3−2+2i32+2i32−2i302-200-221+i3−1−i31−i3−1+i31-100000002-2-221+i3−1−i31−i3−1+i300−1−i31+i3−1+i31−i300000000000001-1−1−i32−1+i32-111+i321−i321+i32−1−i321−i32−1+i3200000
χ414-404-4−2−2i3−2+2i32+2i32−2i30-22002-2−1−i31+i3−1+i31−i31-10000000-22-221+i3−1−i31−i3−1+i3001+i3−1−i31−i3−1+i300000000000001-1−1−i32−1+i321-11+i321−i32−1−i321+i32−1+i321−i3200000
χ424-404-4−2−2i3−2+2i32+2i32−2i30-2200-221+i3−1−i31−i3−1+i31-10000000-222-2−1−i31+i3−1+i31−i3001+i3−1−i31−i3−1+i300000000000001-1−1−i32−1+i32-111+i321−i321+i32−1−i321−i32−1+i3200000
χ43666-1-100006666600000066-1-1-1006-1-1-100000000000000-1-1-100000000-1-1000000000000000
χ44666-1-100006-6-66-600000066-1-1-100-6-1110000000000000011100000000-1-1000000000000000
χ4566-2666666200-2000000000-2-2-2-2-20200222222220000-2-20000-20000-2-200000000000000000
χ4666-2666666200-2000000000-2-2-2-2-20200-2-2-2-2-2-2220000-2-20000200002200000000000000000
χ4766-2666666-2222-200000000-222-2-20-222000000-2-2222222-20000-2-2000000000000000000000
χ4866-2666666-2-2-22200000000-222-2-20-2-2-2000000-2-2-2-2-2-2222000022000000000000000000000
χ4966-266−3+3i3−3−3i3−3+3i3−3−3i3200-2000000000-2-2-21−i31+i3020022−1+i3−1+i3−1−i3−1−i3−1+i3−1−i300001−i31+i30000-200001−i31+i300000000000000000
χ5066-266−3+3i3−3−3i3−3+3i3−3−3i3200-2000000000-2-2-21−i31+i30200-2-21−i31−i31+i31+i3−1+i3−1−i300001−i31+i3000020000−1+i3−1−i300000000000000000
χ5166-266−3+3i3−3−3i3−3+3i3−3−3i3-2222-200000000-2221−i31+i30-2220000001−i31+i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i3-200001−i31+i3000000000000000000000
χ5266-266−3+3i3−3−3i3−3+3i3−3−3i3-2-2-22200000000-2221−i31+i30-2-2-20000001−i31+i31−i31−i31+i31+i3−1+i3−1−i320000−1+i3−1−i3000000000000000000000
χ5366-266−3−3i3−3+3i3−3−3i3−3+3i3200-2000000000-2-2-21+i31−i3020022−1−i3−1−i3−1+i3−1+i3−1−i3−1+i300001+i31−i30000-200001+i31−i300000000000000000
χ5466-266−3−3i3−3+3i3−3−3i3−3+3i3200-2000000000-2-2-21+i31−i30200-2-21+i31+i31−i31−i3−1−i3−1+i300001+i31−i3000020000−1−i3−1+i300000000000000000
χ5566-266−3−3i3−3+3i3−3−3i3−3+3i3-2222-200000000-2221+i31−i30-2220000001+i31−i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3-200001+i31−i3000000000000000000000
χ5666-266−3−3i3−3+3i3−3−3i3−3+3i3-2-2-22200000000-2221+i31−i30-2-2-20000001+i31−i31+i31+i31−i31−i3−1−i3−1+i320000−1−i3−1+i3000000000000000000000
χ578-808-888-8-8000004-44-44-4-110000000000000000000000000000000000-11-1-1-1111-11-1100000
χ588-808-888-8-800000-44-44-44-110000000000000000000000000000000000-11-1-11-1111-11-100000
χ598-808-8−4+4i3−4−4i34−4i34+4i3000004-4−2+2i32−2i3−2−2i32+2i3-110000000000000000000000000000000000-111−i321+i32-11−1+i32−1−i321−i32−1+i321+i32−1−i3200000
χ608-808-8−4+4i3−4−4i34−4i34+4i300000-442−2i3−2+2i32+2i3−2−2i3-110000000000000000000000000000000000-111−i321+i321-1−1+i32−1−i32−1+i321−i32−1−i321+i3200000
χ618-808-8−4−4i3−4+4i34+4i34−4i3000004-4−2−2i32+2i3−2+2i32−2i3-110000000000000000000000000000000000-111+i321−i32-11−1−i32−1+i321+i32−1−i321−i32−1+i3200000
χ628-808-8−4−4i3−4+4i34+4i34−4i300000-442+2i3−2−2i32−2i3−2+2i3-110000000000000000000000000000000000-111+i321−i321-1−1−i32−1+i32−1−i321+i32−1+i321−i3200000
χ63121212-2-200001200120000000-6-6-2-2-2000-200000000000000000000000000011000000000000000
χ64181818-3-30000-666-6600000000-31100-61-1-100000000000000-1110000000000000000000000000
χ65181818-3-30000-6-6-6-6-600000000-311006111000000000000001-1-10000000000000000000000000
χ661818-6-3-30000-6666-6000000001−1−2i7−1+2i70001-1-1000000000000001−i7i70000000000000000000000000
χ671818-6-3-30000-6666-6000000001−1+2i7−1−2i70001-1-1000000000000001i7−i70000000000000000000000000
χ681818-6-3-30000-6-6-666000000001−1−2i7−1+2i700011100000000000000-1i7−i70000000000000000000000000
χ691818-6-3-30000-6-6-666000000001−1+2i7−1−2i700011100000000000000-1−i7i70000000000000000000000000
χ7024-240-440000012-12000000006-60000000-220000000000000000000000000-11000000000000000
χ7124-240-4400000-1212000000006-600000002-20000000000000000000000000-11000000000000000
χ723636-12-6-600001200-12000000000222000-200000000000000000000000000000000000000000000
χ7348-480-88000000000000000-6600000000000000000000000000000000001-1000000000000000

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