Finite Group Databasebeta

← Group #72258629

Character table — Group #72258629

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size11112233336666666666888812121212242424243232323232323232323232323232323248484848484848484848484848484848
order1222222222224444444422224444222236666666666666662444444488888888
χ11111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11-1-111111-1-1-1-1
χ411111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-11111
χ51111-1-11111-1-11111111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11-11-1-11-1111-1-111-1-1
χ61111-1-11111-1-11111111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-11-111-11-1-1-111-1-111
χ71111-1-11111-1-111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-11-1-11111-1-1-1-111
χ81111-1-11111-1-111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-111-111-1-1-1-11111-1-1
χ922222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ1022222222222222222222-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ112222-2-22222-2-22222222222-2-2-2-2-2-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ122222-2-22222-2-222222222-2-222-2-2-2-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ1322-2-2002-2-220022-2-222-2-2002-20000002-222-2-20000000022-2-20000000000000000
χ1422-2-2002-2-220022-2-222-2-2002-20000002-2-1-111−i3−i3i3i3−i3−i3i3i3-1-1110000000000000000
χ1522-2-2002-2-220022-2-222-2-2002-20000002-2-1-111i3i3−i3−i3i3i3−i3−i3-1-1110000000000000000
χ1622-2-2002-2-220022-2-222-2-200-22000000-2222-2-200000000-2-2220000000000000000
χ1722-2-2002-2-220022-2-222-2-200-22000000-22-1-111−i3−i3i3i3i3i3−i3−i311-1-10000000000000000
χ1822-2-2002-2-220022-2-222-2-200-22000000-22-1-111i3i3−i3−i3−i3−i3i3i311-1-10000000000000000
χ192-22-200-22-22002-22-22-22-22-20000002-2002-22-200002-22-200000000000000000000
χ202-22-200-22-22002-22-22-22-22-20000002-200-11-11−i3i3−i3i3-11-11−i3i3−i3i30000000000000000
χ212-22-200-22-22002-22-22-22-22-20000002-200-11-11i3−i3i3−i3-11-11i3−i3i3−i30000000000000000
χ222-22-200-22-22002-22-22-22-2-22000000-22002-22-20000-22-2200000000000000000000
χ232-22-200-22-22002-22-22-22-2-22000000-2200-11-11−i3i3−i3i31-11-1i3−i3i3−i30000000000000000
χ242-22-200-22-22002-22-22-22-2-22000000-2200-11-11i3−i3i3−i31-11-1−i3i3−i3i30000000000000000
χ252-2-222-2-2-2222-22-2-222-2-22000022-2-200002-2-222-2-22000000000000000000000000
χ262-2-222-2-2-2222-22-2-222-2-22000022-2-20000-111-1-111-1−i3i3i3−i3−i3i3i3−i30000000000000000
χ272-2-222-2-2-2222-22-2-222-2-22000022-2-20000-111-1-111-1i3−i3−i3i3i3−i3−i3i30000000000000000
χ282-2-22-22-2-222-222-2-222-2-220000-2-22200002-2-22-222-2000000000000000000000000
χ292-2-22-22-2-222-222-2-222-2-220000-2-2220000-111-11-1-11−i3i3i3−i3i3−i3−i3i30000000000000000
χ302-2-22-22-2-222-222-2-222-2-220000-2-2220000-111-11-1-11i3−i3−i3i3−i3i3i3−i30000000000000000
χ31333333333333-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-1000000000000000011111111-1-1-1-1-1-1-1-1
χ32333333333333-1-1-1-1-1-1-1-13333-1-1-1-1-1-1-1-10000000000000000-1-1-1-1-1-1-1-111111111
χ33333333333333-1-1-1-1-1-1-1-1-3-3-3-3-1-1-1-11111000000000000000011-1-11-1-11-1-1-1-11111
χ34333333333333-1-1-1-1-1-1-1-1-3-3-3-3-1-1-1-111110000000000000000-1-111-111-11111-1-1-1-1
χ353333-3-33333-3-3-1-1-1-1-1-1-1-133-3-31111-1-11100000000000000001-11-1-11-11-1-111-1-111
χ363333-3-33333-3-3-1-1-1-1-1-1-1-133-3-31111-1-1110000000000000000-11-111-11-111-1-111-1-1
χ373333-3-33333-3-3-1-1-1-1-1-1-1-1-3-333111111-1-100000000000000001-1-11-1-111-1-11111-1-1
χ383333-3-33333-3-3-1-1-1-1-1-1-1-1-3-333111111-1-10000000000000000-111-111-1-111-1-1-1-111
χ39666666-2-2-2-2-2-22-2-22-222-200002-22-2000000000000000000002200-200-200000000
χ40666666-2-2-2-2-2-22-2-22-222-200002-22-200000000000000000000-2-200200200000000
χ41666666-2-2-2-2-2-2-222-22-2-220000-22-220000000000000000000000220-2-2000000000
χ42666666-2-2-2-2-2-2-222-22-2-220000-22-220000000000000000000000-2-2022000000000
χ436666-6-6-2-2-2-2222-2-22-222-20000-22-22000000000000000000002-200200-200000000
χ446666-6-6-2-2-2-2222-2-22-222-20000-22-2200000000000000000000-2200-200200000000
χ456666-6-6-2-2-2-222-222-22-2-2200002-22-200000000000000000000002-20-22000000000
χ466666-6-6-2-2-2-222-222-22-2-2200002-22-20000000000000000000000-2202-2000000000
χ4766-6-6006-6-6600-2-222-2-222006-6000000-2200000000000000000000000000000000
χ4866-6-6006-6-6600-2-222-2-22200-660000002-200000000000000000000000000000000
χ496-66-600-66-6600-22-22-22-226-6000000-220000000000000000000000000000000000
χ506-66-600-66-6600-22-22-22-22-660000002-20000000000000000000000000000000000
χ516-6-666-622-2-2-222222-2-2-2-200002-2-2200000000000000000000000000002i−2i2i−2i0000
χ526-6-666-622-2-2-222222-2-2-2-200002-2-220000000000000000000000000000−2i2i−2i2i0000
χ536-6-666-622-2-2-22-2-2-2-222220000-222-2000000000000000000000000000000002-22-2
χ546-6-666-622-2-2-22-2-2-2-222220000-222-200000000000000000000000000000000-22-22
χ556-6-666-6-6-6666-6-222-2-222-20000-2-222000000000000000000000000000000000000
χ566-6-66-6622-2-22-22222-2-2-2-20000-222-200000000000000000000000000002i−2i−2i2i0000
χ576-6-66-6622-2-22-22222-2-2-2-20000-222-20000000000000000000000000000−2i2i2i−2i0000
χ586-6-66-6622-2-22-2-2-2-2-2222200002-2-22000000000000000000000000000000002-2-22
χ596-6-66-6622-2-22-2-2-2-2-2222200002-2-2200000000000000000000000000000000-222-2
χ606-6-66-66-6-666-66-222-2-222-2000022-2-2000000000000000000000000000000000000
χ611212-12-1200-444-4004-44-4-44-4400000000000000000000000000000000000000000000
χ621212-12-1200-444-400-44-444-44-400000000000000000000000000000000000000000000
χ6312-1212-12004-44-40044-4-4-4-44400000000000000000000000000000000000000000000
χ6412-1212-12004-44-400-4-44444-4-400000000000000000000000000000000000000000000

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