Finite Group Databasebeta

← Group #72239924

Character table — Group #72239924

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size112333333333333336666666666666666666666666666666666648484848484848484848484848484848128128128128
order12422222244444444224444444444444444444444444444444444444444488888888361212
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ311-11111111111111111-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11-11111-1-1-1-111-1-1
χ411-11111111111111111-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-11-1-1-1-1111111-1-1
χ522222222222222222222222222222222222222222222222222220000000000000000-1-1-1-1
χ622-22222222222222222-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-1-111
χ72-20222-2-2-22222-2-2-2-22-200000222222-2-2-2-2-2-2000000000000000000000000000000002-200
χ82-20222-2-2-22222-2-2-2-22-200000222222-2-2-2-2-2-200000000000000000000000000000000-113−3
χ92-20222-2-2-22222-2-2-2-22-200000222222-2-2-2-2-2-200000000000000000000000000000000-11−33
χ10333333333-1-1-1-1-1-1-1-13333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-10000
χ11333333333-1-1-1-1-1-1-1-13333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111110000
χ123333-1-13-1-1−1+2i−1+2i−1−2i−1−2i−1+2i−1+2i−1−2i−1−2i-1-13-1-1-1-11111−1+2i−1−2i1111−1+2i−1−2i11111111−1+2i−1+2i−1+2i−1+2i−1−2i−1−2i−1−2i−1−2i111-11-1-1-1ii−i−iii−i−i0000
χ133333-1-13-1-1−1+2i−1+2i−1−2i−1−2i−1+2i−1+2i−1−2i−1−2i-1-13-1-1-1-11111−1+2i−1−2i1111−1+2i−1−2i11111111−1+2i−1+2i−1+2i−1+2i−1−2i−1−2i−1−2i−1−2i-1-1-11-1111−i−iii−i−iii0000
χ143333-1-13-1-1−1−2i−1−2i−1+2i−1+2i−1−2i−1−2i−1+2i−1+2i-1-13-1-1-1-11111−1−2i−1+2i1111−1−2i−1+2i11111111−1−2i−1−2i−1−2i−1−2i−1+2i−1+2i−1+2i−1+2i111-11-1-1-1−i−iii−i−iii0000
χ153333-1-13-1-1−1−2i−1−2i−1+2i−1+2i−1−2i−1−2i−1+2i−1+2i-1-13-1-1-1-11111−1−2i−1+2i1111−1−2i−1+2i11111111−1−2i−1−2i−1−2i−1−2i−1+2i−1+2i−1+2i−1+2i-1-1-11-1111ii−i−iii−i−i0000
χ16333-13-1-13-1−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i-1-1-13-1-1-111−1+2i−1−2i1111−1+2i−1−2i111111−1+2i−1+2i−1−2i−1−2i11−1+2i−1−2i11−1+2i−1−2i11-11-11-1-1i−ii−ii−ii−i0000
χ17333-13-1-13-1−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i-1-1-13-1-1-111−1+2i−1−2i1111−1+2i−1−2i111111−1+2i−1+2i−1−2i−1−2i11−1+2i−1−2i11−1+2i−1−2i-1-11-11-111−ii−ii−ii−ii0000
χ18333-13-1-13-1−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i-1-1-13-1-1-111−1−2i−1+2i1111−1−2i−1+2i111111−1−2i−1−2i−1+2i−1+2i11−1−2i−1+2i11−1−2i−1+2i11-11-11-1-1−ii−ii−ii−ii0000
χ19333-13-1-13-1−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i-1-1-13-1-1-111−1−2i−1+2i1111−1−2i−1+2i111111−1−2i−1−2i−1+2i−1+2i11−1−2i−1+2i11−1−2i−1+2i-1-11-11-111i−ii−ii−ii−i0000
χ20333-1-13-1-133-1-133-1-13-1-1-1-13-1-13-1-1-1-1-13-1-1-1-1-133-1-1-1-1-1-1-1-13-1-1-1-1311-1-1-1-1111-1-111-1-110000
χ21333-1-13-1-133-1-133-1-13-1-1-1-13-1-13-1-1-1-1-13-1-1-1-1-133-1-1-1-1-1-1-1-13-1-1-1-13-1-11111-1-1-111-1-111-10000
χ22333-1-13-1-13-133-1-133-1-1-1-1-13-1-1-13-1-1-1-1-13-1-1-1-1-1-133-1-1-1-1-1-1-13-1-13-111-1-1-1-111-111-1-111-10000
χ23333-1-13-1-13-133-1-133-1-1-1-1-13-1-1-13-1-1-1-1-13-1-1-1-1-1-133-1-1-1-1-1-1-13-1-13-1-1-11111-1-11-1-111-1-110000
χ2433-3333333-1-1-1-1-1-1-1-133-3-3-3-3-3-1-1-1-1-1-1-1-1-1-1-1-111111111111111111-111-1-11-1-1-1-1-111110000
χ2533-3333333-1-1-1-1-1-1-1-133-3-3-3-3-3-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-11-1-111-111111-1-1-1-10000
χ2633-33-1-13-1-1−1+2i−1+2i−1−2i−1−2i−1+2i−1+2i−1−2i−1−2i-1-1-311111111−1+2i−1−2i1111−1+2i−1−2i-1-1-1-1-1-1-1-11−2i1−2i1−2i1−2i1+2i1+2i1+2i1+2i1-11-1-11-11ii−i−i−i−iii0000
χ2733-33-1-13-1-1−1+2i−1+2i−1−2i−1−2i−1+2i−1+2i−1−2i−1−2i-1-1-311111111−1+2i−1−2i1111−1+2i−1−2i-1-1-1-1-1-1-1-11−2i1−2i1−2i1−2i1+2i1+2i1+2i1+2i-11-111-11-1−i−iiiii−i−i0000
χ2833-33-1-13-1-1−1−2i−1−2i−1+2i−1+2i−1−2i−1−2i−1+2i−1+2i-1-1-311111111−1−2i−1+2i1111−1−2i−1+2i-1-1-1-1-1-1-1-11+2i1+2i1+2i1+2i1−2i1−2i1−2i1−2i1-11-1-11-11−i−iiiii−i−i0000
χ2933-33-1-13-1-1−1−2i−1−2i−1+2i−1+2i−1−2i−1−2i−1+2i−1+2i-1-1-311111111−1−2i−1+2i1111−1−2i−1+2i-1-1-1-1-1-1-1-11+2i1+2i1+2i1+2i1−2i1−2i1−2i1−2i-11-111-11-1ii−i−i−i−iii0000
χ3033-3-13-1-13-1−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i-1-11-311111−1+2i−1−2i1111−1+2i−1−2i11-1-1-1-11−2i1−2i1+2i1+2i-1-11−2i1+2i-1-11−2i1+2i1-1-111-1-11i−ii−i−ii−ii0000
χ3133-3-13-1-13-1−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i-1-11-311111−1+2i−1−2i1111−1+2i−1−2i11-1-1-1-11−2i1−2i1+2i1+2i-1-11−2i1+2i-1-11−2i1+2i-111-1-111-1−ii−iii−ii−i0000
χ3233-3-13-1-13-1−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i-1-11-311111−1−2i−1+2i1111−1−2i−1+2i11-1-1-1-11+2i1+2i1−2i1−2i-1-11+2i1−2i-1-11+2i1−2i1-1-111-1-11−ii−iii−ii−i0000
χ3333-3-13-1-13-1−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i−1−2i−1+2i-1-11-311111−1−2i−1+2i1111−1−2i−1+2i11-1-1-1-11+2i1+2i1−2i1−2i-1-11+2i1−2i-1-11+2i1−2i-111-1-111-1i−ii−i−ii−ii0000
χ3433-3-1-13-1-133-1-133-1-13-1-111-3113-1-1-1-1-13-1-1-1-1-1-3-311111111-31111-31-1-1-1111-11-1-11-111-10000
χ3533-3-1-13-1-133-1-133-1-13-1-111-3113-1-1-1-1-13-1-1-1-1-1-3-311111111-31111-3-1111-1-1-11-111-11-1-110000
χ3633-3-1-13-1-13-133-1-133-1-1-111-311-13-1-1-1-1-13-1-1-1-111-3-31111111-311-311-1-1-1111-1-111-11-1-110000
χ3733-3-1-13-1-13-133-1-133-1-1-111-311-13-1-1-1-1-13-1-1-1-111-3-31111111-311-31-1111-1-1-111-1-11-111-10000
χ386666-2-26-2-222222222-2-26-2-2-2-2-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-22222222200000000000000000000
χ39666-26-2-26-222222222-2-2-26-2-2-2-2-222-2-2-2-222-2-2-2-2-2-22222-2-222-2-22200000000000000000000
χ40666-2-26-2-26-2-2-2-2-2-2-2-2-2-2-2-26-2-2-2-22222-2-22222-2-2-2-2222222-2-222-2-200000000000000000000
χ41666-2-2-2-2-2-22−2+4i−2−4i22−2+4i−2−4i222-2-2-222-222i−2i−2i2i-222i−2i−2i2i-2-2222i2i−2i−2i−2i−2i2−2+4i2i2i−2−4i200000000000000000000
χ42666-2-2-2-2-2-22−2−4i−2+4i22−2−4i−2+4i222-2-2-222-22−2i2i2i−2i-22−2i2i2i−2i-2-222−2i−2i2i2i2i2i2−2−4i−2i−2i−2+4i200000000000000000000
χ43666-2-2-2-2-2-2−2+4i22−2−4i−2+4i22−2−4i22-2-2-2222-2−2i2i−2i2i2-2−2i2i−2i2i22-2-2−2i−2i2i2i−2i−2i−2+4i22i2i2−2−4i00000000000000000000
χ44666-2-2-2-2-2-2−2−4i22−2+4i−2−4i22−2+4i22-2-2-2222-22i−2i2i−2i2-22i−2i2i−2i22-2-22i2i−2i−2i2i2i−2−4i2−2i−2i2−2+4i00000000000000000000
χ4566-66-2-26-2-222222222-2-2-62222-2-2-2-222-2-2-2-22222222222-2-2-2-2-2-2-2-200000000000000000000
χ4666-6-26-2-26-222222222-2-22-6222-2-222-2-2-2-222-2-22222-2-2-2-222-2-222-2-200000000000000000000
χ4766-6-2-26-2-26-2-2-2-2-2-2-2-2-2-222-622-2-22222-2-222222222-2-2-2-2-2-222-2-22200000000000000000000
χ4866-6-2-2-2-2-2-22−2+4i−2−4i22−2+4i−2−4i222222-2-2-222i−2i−2i2i-222i−2i−2i2i22-2-2−2i−2i2i2i2i2i-22−4i−2i−2i2+4i-200000000000000000000
χ4966-6-2-2-2-2-2-22−2−4i−2+4i22−2−4i−2+4i222222-2-2-22−2i2i2i−2i-22−2i2i2i−2i22-2-22i2i−2i−2i−2i−2i-22+4i2i2i2−4i-200000000000000000000
χ5066-6-2-2-2-2-2-2−2+4i22−2−4i−2+4i22−2−4i22222-2-22-2−2i2i−2i2i2-2−2i2i−2i2i-2-2222i2i−2i−2i2i2i2−4i-2−2i−2i-22+4i00000000000000000000
χ5166-6-2-2-2-2-2-2−2−4i22−2+4i−2−4i22−2+4i22222-2-22-22i−2i2i−2i2-22i−2i2i−2i-2-222−2i−2i2i2i−2i−2i2+4i-22i2i-22−4i00000000000000000000
χ526-60666-6-6-6-2-2-2-222226-600000-2-2-2-2-2-2222222000000000000000000000000000000000000
χ536-606-2-2-6222222-2-2-2-2-2200000-2-2-2-2222222-2-24-44-44-44-40000000000000000000000000000
χ546-606-2-2-6222222-2-2-2-2-2200000-2-2-2-2222222-2-2-44-44-44-440000000000000000000000000000
χ556-606-2-2-622−2+4i−2+4i−2−4i−2−4i2−4i2−4i2+4i2+4i-22000002222−2+4i−2−4i-2-2-2-22−4i2+4i000000000000000000000000000000000000
χ566-606-2-2-622−2−4i−2−4i−2+4i−2+4i2+4i2+4i2−4i2−4i-22000002222−2−4i−2+4i-2-2-2-22+4i2−4i000000000000000000000000000000000000
χ576-60-26-22-622222-2-2-2-2-2200000-2-222-2-222-2-2224-4-4400004-4004-40000000000000000000000
χ586-60-26-22-622222-2-2-2-2-2200000-2-222-2-222-2-222-444-40000-4400-440000000000000000000000
χ596-60-26-22-62−2+4i−2−4i−2+4i−2−4i2−4i2+4i2−4i2+4i-220000022−2+4i−2−4i22-2-22−4i2+4i-2-2000000000000000000000000000000000000
χ606-60-26-22-62−2−4i−2+4i−2−4i−2+4i2+4i2−4i2+4i2−4i-220000022−2−4i−2+4i22-2-22+4i2−4i-2-2000000000000000000000000000000000000
χ616-60-2-2622-66-2-26-622-6-22000006-2-2-2-2-2-622222000000000000000000000000000000000000
χ626-60-2-2622-6-266-22-6-62-2200000-26-2-2-2-22-62222000000000000000000000000000000000000
χ636-60-2-2622-6-2-2-2-22222-2200000-2-2222222-2-2-2-200004i−4i−4i4i4i−4i00−4i4i0000000000000000000000
χ646-60-2-2622-6-2-2-2-22222-2200000-2-2222222-2-2-2-20000−4i4i4i−4i−4i4i004i−4i0000000000000000000000
χ656-60-2-2-22222−2+4i−2−4i2-22−4i2+4i-22-20004i−4i-222i−2i−2i2i2-2−2i2i2i−2i4-400−2−2i2+2i−2+2i2−2i−2+2i2−2i00−2−2i2+2i0000000000000000000000
χ666-60-2-2-22222−2+4i−2−4i2-22−4i2+4i-22-2000−4i4i-222i−2i−2i2i2-2−2i2i2i−2i-44002+2i−2−2i2−2i−2+2i2−2i−2+2i002+2i−2−2i0000000000000000000000
χ676-60-2-2-22222−2−4i−2+4i2-22+4i2−4i-22-20004i−4i-22−2i2i2i−2i2-22i−2i−2i2i-44002−2i−2+2i2+2i−2−2i2+2i−2−2i002−2i−2+2i0000000000000000000000
χ686-60-2-2-22222−2−4i−2+4i2-22+4i2−4i-22-2000−4i4i-22−2i2i2i−2i2-22i−2i−2i2i4-400−2+2i2−2i−2−2i2+2i−2−2i2+2i00−2+2i2−2i0000000000000000000000
χ696-60-2-2-2222−2+4i22−2−4i2−4i-2-22+4i2-20004i−4i2-2−2i2i−2i2i-222i−2i2i−2i004-4−2+2i2−2i−2−2i2+2i2−2i−2+2i002+2i−2−2i0000000000000000000000
χ706-60-2-2-2222−2+4i22−2−4i2−4i-2-22+4i2-2000−4i4i2-2−2i2i−2i2i-222i−2i2i−2i00-442−2i−2+2i2+2i−2−2i−2+2i2−2i00−2−2i2+2i0000000000000000000000
χ716-60-2-2-2222−2−4i22−2+4i2+4i-2-22−4i2-20004i−4i2-22i−2i2i−2i-22−2i2i−2i2i00-442+2i−2−2i2−2i−2+2i−2−2i2+2i00−2+2i2−2i0000000000000000000000
χ726-60-2-2-2222−2−4i22−2+4i2+4i-2-22−4i2-2000−4i4i2-22i−2i2i−2i-22−2i2i−2i2i004-4−2−2i2+2i−2+2i2−2i2+2i−2−2i002−2i−2+2i0000000000000000000000

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