Finite Group Databasebeta

← Group #13155125

Character table — Group #13155125

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size112224444444444888888888888888888888363636363636727272727272727272727272727272727272
order1223623366666663366666666666666666662444664444412121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-111-111-1-11-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-111-1-1-1111-1-1-1-1-1-1-1-11111
χ511111-11111111-1-111-11-1-1-1111111-1-1-1-1-1-1-1-1-1111-1-1-1i−ii−i111-1-1ii−i−iii−i−i
χ611111-11111111-1-111-11-1-1-1111111-1-1-1-1-1-1-1-1-1111-1-1-1−ii−ii111-1-1−i−iii−i−iii
χ711111-11111111-1-111-11-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1-1-11i−i−ii1-1-111ii−i−i−i−iii
χ811111-11111111-1-111-11-1-1-1111111-1-1-1-1-1-1-1-1-11-1-1-1-11−iii−i1-1-111−i−iiiii−i−i
χ9222222222222222222222222222222222222-2-200-2-200000-2000000000000
χ1022222-22222222-2-222-22-2-2-2222222-2-2-2-2-2-2-2-22-2002200000-2000000000000
χ11222-1-1222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-12200-1-100022-100000000-1-1-1-1
χ12222-1-1222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-12200-1-1000-2-2-1000000001111
χ13222-1-1222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20011000001000000003−33−3
χ14222-1-1222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2001100000100000000−33−33
χ15222-1-1-222-12222-2-2-1-112-2-2-2-1-1-1-1-1-1111111112-200-1-100000100000000−i3i3i3−i3
χ16222-1-1-222-12222-2-2-1-112-2-2-2-1-1-1-1-1-1111111112-200-1-100000100000000i3−i3−i3i3
χ17222-1-1-222-12222-2-2-1-112-2-2-2-1-1-1-1-1-111111111-2200110002i−2i-100000000−i−iii
χ18222-1-1-222-12222-2-2-1-112-2-2-2-1-1-1-1-1-111111111-220011000−2i2i-100000000ii−i−i
χ194444441-241-211-2-21-24-211-2111-2-2-21111-2-2-2-2002200200000-1-1-1-100000000
χ204444441-241-211-2-21-24-211-2111-2-2-21111-2-2-2-200-2-200-200000111100000000
χ21444444-214-21-2-211-2141-2-21-2-2-2111-2-2-2-211110000000220000000-1-1-1-10000
χ22444444-214-21-2-211-2141-2-21-2-2-2111-2-2-2-211110000000-2-2000000011110000
χ2344444-41-241-211221-2-4-2-1-12111-2-2-2-1-1-1-12222002200-200000-1-11100000000
χ2444444-41-241-211221-2-4-2-1-12111-2-2-2-1-1-1-1222200-2-20020000011-1-100000000
χ2544444-4-214-21-2-2-1-1-21-4122-1-2-2-21112222-1-1-1-100000002i−2i0000000−i−iii0000
χ2644444-4-214-21-2-2-1-1-21-4122-1-2-2-21112222-1-1-1-10000000−2i2i0000000ii−i−i0000
χ2744-444044-4-444-400440-40004-4-44-4-400000000000000000000000000000000
χ2844-4440-21-421-2233-210-100-3-2221-1-1000033-3-300000000000000003−33−30000
χ2944-4440-21-421-2233-210-100-3-2221-1-1000033-3-30000000000000000−33−330000
χ3044-4440-21-421-22-3-3-210-1003-2221-1-10000-3-3330000000000000000−i3i3i3−i30000
χ3144-4440-21-421-22-3-3-210-1003-2221-1-10000-3-3330000000000000000i3−i3−i3i30000
χ3244-4-2-20442-444-400-2-20-4000-222-222000000000000−2i32i3000000000000000000
χ3344-4-2-20442-444-400-2-20-4000-222-2220000000000002i3−2i3000000000000000000
χ344-404-401-20-32-13−2i32i31-200−i3i30-13-3200−i3−i3i3i3−2i32i300002i−2i00000000i−i3−300000000
χ354-404-401-20-32-13−2i32i31-200−i3i30-13-3200−i3−i3i3i3−2i32i30000−2i2i00000000−ii−3300000000
χ364-404-401-20-32-132i3−2i31-200i3−i30-13-3200i3i3−i3−i32i3−2i300002i−2i00000000i−i−3300000000
χ374-404-401-20-32-132i3−2i31-200i3−i30-13-3200i3i3−i3−i32i3−2i30000−2i2i00000000−ii3−300000000
χ384-404-404400-4-40004400000-400-40000000000002i−2i00000000−2i2i0000000000
χ394-404-404400-4-40004400000-400-4000000000000−2i2i000000002i−2i0000000000
χ40888-4-482-4-42-422-4-4-12-4-422-4-1-1-1222-1-1-1-12222000000000000000000000000
χ41888-4-48-42-4-42-4-4222-1-42-4-42222-1-1-12222-1-1-1-1000000000000000000000000
χ42888-4-4-82-4-42-42244-124-4-2-24-1-1-12221111-2-2-2-2000000000000000000000000
χ43888-4-4-8-42-4-42-4-4-2-22-14244-2222-1-1-1-2-2-2-21111000000000000000000000000
χ4488-88802-4-8-2-42-2002-4040002-2-2-44400000000000000000000000000000000
χ4588-8-4-402-44-2-42-200-1204000-1112-2-2−3i33i3−3i33i30000000000000000000000000000
χ4688-8-4-402-44-2-42-200-1204000-1112-2-23i3−3i33i3−3i30000000000000000000000000000
χ4788-8-4-40-42442-44662-10-200-62-2-2-1110000-3-333000000000000000000000000
χ4888-8-4-40-42442-44-6-62-10-20062-2-2-111000033-3-3000000000000000000000000
χ498-808-802-4064-2-6002-400000-2-6640000000000000000000000000000000000
χ508-808-80-4200-240−2i32i3-42002i3−2i30400-2002i32i3−2i3−2i3−2i32i300000000000000000000000000
χ518-808-80-4200-2402i3−2i3-4200−2i32i30400-200−2i3−2i32i32i32i3−2i300000000000000000000000000
χ528-80-4402-4064-2-600-120000013-3-2003-3-33006-6000000000000000000000000
χ538-80-4402-4064-2-600-120000013-3-200-333-300-66000000000000000000000000
χ548-80-4402-40-64-26−4i34i3-1200−2i32i301-33-200i3i3−i3−i32i3−2i300000000000000000000000000
χ558-80-4402-40-64-264i3−4i3-12002i3−2i301-33-200−i3−i3i3i3−2i32i300000000000000000000000000
χ568-80-4408800-8-8000-4-40000040040000000000000000000000000000000000
χ578-80-440-4200-240−2i32i32-1002i3−2i30-2001−3i33i33−i3−3−i3−3+i33+i3i3−i3-33000000000000000000000000
χ588-80-440-4200-240−2i32i32-1002i3−2i30-20013i3−3i3−3−i33−i33+i3−3+i3i3−i33-3000000000000000000000000
χ598-80-440-4200-2402i3−2i32-100−2i32i30-2001−3i33i3−3+i33+i33−i3−3−i3−i3i33-3000000000000000000000000
χ608-80-440-4200-2402i3−2i32-100−2i32i30-20013i3−3i33+i3−3+i3−3−i33−i3−i3i3-33000000000000000000000000

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