Finite Group Databasebeta

← Group #72231147

Character table — Group #72231147

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1133333366666612121212121224242424242424244848484812812811333333666666121212121212242424242424242448484848128128
order12222222224444444444888888884444362222222222444444444488888888444466
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ322222222222222222222000000000000-1-122222222222222222222000000000000-1-1
χ42-2222-2-2-22-200000000002222−2−2−2−20000-112-2222-2-2-22-200000000002222−2−2−2−20000-11
χ52-2222-2-2-22-20000000000−2−2−2−222220000-112-2222-2-2-22-20000000000−2−2−2−222220000-11
χ63333333333-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1003333333333-1-1-1-1-1-1-1-1-1-111111111-1-1-1-100
χ73333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111003333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111100
χ8333-1-13-1-1-1-1−1+2i−1+2i−1−2i−1−2i1111−1+2i−1−2iii−i−iii−i−i-11-1100333-1-13-1-1-1-1−1+2i−1+2i−1−2i−1−2i1111−1+2i−1−2iii−i−iii−i−i-11-1100
χ9333-1-13-1-1-1-1−1+2i−1+2i−1−2i−1−2i1111−1+2i−1−2i−i−iii−i−iii1-11-100333-1-13-1-1-1-1−1+2i−1+2i−1−2i−1−2i1111−1+2i−1−2i−i−iii−i−iii1-11-100
χ10333-1-13-1-1-1-1−1−2i−1−2i−1+2i−1+2i1111−1−2i−1+2iii−i−iii−i−i1-11-100333-1-13-1-1-1-1−1−2i−1−2i−1+2i−1+2i1111−1−2i−1+2iii−i−iii−i−i1-11-100
χ11333-1-13-1-1-1-1−1−2i−1−2i−1+2i−1+2i1111−1−2i−1+2i−i−iii−i−iii-11-1100333-1-13-1-1-1-1−1−2i−1−2i−1+2i−1+2i1111−1−2i−1+2i−i−iii−i−iii-11-1100
χ1233-13-1-13-1-1-1−1+2i−1−2i−1+2i−1−2i11−1+2i−1−2i11i−ii−ii−ii−i-1-1110033-13-1-13-1-1-1−1+2i−1−2i−1+2i−1−2i11−1+2i−1−2i11i−ii−ii−ii−i-1-11100
χ1333-13-1-13-1-1-1−1+2i−1−2i−1+2i−1−2i11−1+2i−1−2i11−ii−ii−ii−ii11-1-10033-13-1-13-1-1-1−1+2i−1−2i−1+2i−1−2i11−1+2i−1−2i11−ii−ii−ii−ii11-1-100
χ1433-13-1-13-1-1-1−1−2i−1+2i−1−2i−1+2i11−1−2i−1+2i11i−ii−ii−ii−i11-1-10033-13-1-13-1-1-1−1−2i−1+2i−1−2i−1+2i11−1−2i−1+2i11i−ii−ii−ii−i11-1-100
χ1533-13-1-13-1-1-1−1−2i−1+2i−1−2i−1+2i11−1−2i−1+2i11−ii−ii−ii−ii-1-1110033-13-1-13-1-1-1−1−2i−1+2i−1−2i−1+2i11−1−2i−1+2i11−ii−ii−ii−ii-1-11100
χ1633-1-13-1-13-1-13-1-133-1-1-1-1-11-1-111-1-111-1-110033-1-13-1-13-1-13-1-133-1-1-1-1-11-1-111-1-111-1-1100
χ1733-1-13-1-13-1-13-1-133-1-1-1-1-1-111-1-111-1-111-10033-1-13-1-13-1-13-1-133-1-1-1-1-1-111-1-111-1-111-100
χ1833-1-13-1-13-1-1-133-1-13-1-1-1-11-1-111-1-11-111-10033-1-13-1-13-1-1-133-1-13-1-1-1-11-1-111-1-11-111-100
χ1933-1-13-1-13-1-1-133-1-13-1-1-1-1-111-1-111-11-1-110033-1-13-1-13-1-1-133-1-13-1-1-1-1-111-1-111-11-1-1100
χ204-4444-4-4-44-400000000000000000000001-14-4444-4-4-44-400000000000000000000001-1
χ21666-2-26-2-2-2-22222-2-2-2-22200000000000000666-2-26-2-2-2-22222-2-2-2-22200000000000000
χ2266-26-2-26-2-2-22222-2-222-2-20000000000000066-26-2-26-2-2-22222-2-222-2-200000000000000
χ2366-2-26-2-26-2-2-2-2-2-2-2-222220000000000000066-2-26-2-26-2-2-2-2-2-2-2-2222200000000000000
χ2466-2-2-2-2-2-2222−2+4i−2−4i2-222i−2i−2i2i0000000000000066-2-2-2-2-2-2222−2+4i−2−4i2-222i−2i−2i2i00000000000000
χ2566-2-2-2-2-2-2222−2−4i−2+4i2-22−2i2i2i−2i0000000000000066-2-2-2-2-2-2222−2−4i−2+4i2-22−2i2i2i−2i00000000000000
χ2666-2-2-2-2-2-222−2+4i22−2−4i2-2−2i2i−2i2i0000000000000066-2-2-2-2-2-222−2+4i22−2−4i2-2−2i2i−2i2i00000000000000
χ2766-2-2-2-2-2-222−2−4i22−2+4i2-22i−2i2i−2i0000000000000066-2-2-2-2-2-222−2−4i22−2+4i2-22i−2i2i−2i00000000000000
χ286-66-2-2-622-220000000000i2i2−i2−i2−i2−i2i2i20000006-66-2-2-622-220000000000i2i2−i2−i2−i2−i2i2i2000000
χ296-66-2-2-622-220000000000−i2−i2i2i2i2i2−i2−i20000006-66-2-2-622-220000000000−i2−i2i2i2i2i2−i2−i2000000
χ306-6-26-22-62-220000000000i2−i2i2−i2−i2i2−i2i20000006-6-26-22-62-220000000000i2−i2i2−i2−i2i2−i2i2000000
χ316-6-26-22-62-220000000000−i2i2−i2i2i2−i2i2−i20000006-6-26-22-62-220000000000−i2i2−i2i2i2−i2i2−i2000000
χ326-6-2-2622-6-2200000000002−2−22−222−20000006-6-2-2622-6-2200000000002−2−22−222−2000000
χ336-6-2-2622-6-220000000000−222−22−2−220000006-6-2-2622-6-220000000000−222−22−2−22000000
χ3412-12-4-4-44444-400000000000000000000000012-12-4-4-44444-4000000000000000000000000
χ351111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ3722222222222222222222000000000000-1-1-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000011
χ382-2222-2-2-22-200000000002222−2−2−2−20000-11-22-2-2-2222-220000000000−2−2−2−2222200001-1
χ392-2222-2-2-22-20000000000−2−2−2−222220000-11-22-2-2-2222-2200000000002222−2−2−2−200001-1
χ403333333333-1-1-1-1-1-1-1-1-1-111111111-1-1-1-100-3-3-3-3-3-3-3-3-3-31111111111-1-1-1-1-1-1-1-1111100
χ413333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111100-3-3-3-3-3-3-3-3-3-3111111111111111111-1-1-1-100
χ42333-1-13-1-1-1-1−1+2i−1+2i−1−2i−1−2i1111−1+2i−1−2iii−i−iii−i−i-11-1100-3-3-311-311111−2i1−2i1+2i1+2i-1-1-1-11−2i1+2i−i−iii−i−iii1-11-100
χ43333-1-13-1-1-1-1−1+2i−1+2i−1−2i−1−2i1111−1+2i−1−2i−i−iii−i−iii1-11-100-3-3-311-311111−2i1−2i1+2i1+2i-1-1-1-11−2i1+2iii−i−iii−i−i-11-1100
χ44333-1-13-1-1-1-1−1−2i−1−2i−1+2i−1+2i1111−1−2i−1+2iii−i−iii−i−i1-11-100-3-3-311-311111+2i1+2i1−2i1−2i-1-1-1-11+2i1−2i−i−iii−i−iii-11-1100
χ45333-1-13-1-1-1-1−1−2i−1−2i−1+2i−1+2i1111−1−2i−1+2i−i−iii−i−iii-11-1100-3-3-311-311111+2i1+2i1−2i1−2i-1-1-1-11+2i1−2iii−i−iii−i−i1-11-100
χ4633-13-1-13-1-1-1−1+2i−1−2i−1+2i−1−2i11−1+2i−1−2i11i−ii−ii−ii−i-1-11100-3-31-311-31111−2i1+2i1−2i1+2i-1-11−2i1+2i-1-1−ii−ii−ii−ii11-1-100
χ4733-13-1-13-1-1-1−1+2i−1−2i−1+2i−1−2i11−1+2i−1−2i11−ii−ii−ii−ii11-1-100-3-31-311-31111−2i1+2i1−2i1+2i-1-11−2i1+2i-1-1i−ii−ii−ii−i-1-11100
χ4833-13-1-13-1-1-1−1−2i−1+2i−1−2i−1+2i11−1−2i−1+2i11i−ii−ii−ii−i11-1-100-3-31-311-31111+2i1−2i1+2i1−2i-1-11+2i1−2i-1-1−ii−ii−ii−ii-1-11100
χ4933-13-1-13-1-1-1−1−2i−1+2i−1−2i−1+2i11−1−2i−1+2i11−ii−ii−ii−ii-1-11100-3-31-311-31111+2i1−2i1+2i1−2i-1-11+2i1−2i-1-1i−ii−ii−ii−i11-1-100
χ5033-1-13-1-13-1-13-1-133-1-1-1-1-11-1-111-1-111-1-1100-3-311-311-311-311-3-311111-111-1-111-1-111-100
χ5133-1-13-1-13-1-13-1-133-1-1-1-1-1-111-1-111-1-111-100-3-311-311-311-311-3-3111111-1-111-1-111-1-1100
χ5233-1-13-1-13-1-1-133-1-13-1-1-1-11-1-111-1-11-111-100-3-311-311-3111-3-311-31111-111-1-111-11-1-1100
χ5333-1-13-1-13-1-1-133-1-13-1-1-1-1-111-1-111-11-1-1100-3-311-311-3111-3-311-311111-1-111-1-11-111-100
χ544-4444-4-4-44-400000000000000000000001-1-44-4-4-4444-440000000000000000000000-11
χ55666-2-26-2-2-2-22222-2-2-2-22200000000000000-6-6-622-62222-2-2-2-22222-2-200000000000000
χ5666-26-2-26-2-2-22222-2-222-2-200000000000000-6-62-622-6222-2-2-2-222-2-22200000000000000
χ5766-2-26-2-26-2-2-2-2-2-2-2-2222200000000000000-6-622-622-622222222-2-2-2-200000000000000
χ5866-2-2-2-2-2-2222−2+4i−2−4i2-222i−2i−2i2i00000000000000-6-6222222-2-2-22−4i2+4i-22-2−2i2i2i−2i00000000000000
χ5966-2-2-2-2-2-2222−2−4i−2+4i2-22−2i2i2i−2i00000000000000-6-6222222-2-2-22+4i2−4i-22-22i−2i−2i2i00000000000000
χ6066-2-2-2-2-2-222−2+4i22−2−4i2-2−2i2i−2i2i00000000000000-6-6222222-2-22−4i-2-22+4i-222i−2i2i−2i00000000000000
χ6166-2-2-2-2-2-222−2−4i22−2+4i2-22i−2i2i−2i00000000000000-6-6222222-2-22+4i-2-22−4i-22−2i2i−2i2i00000000000000
χ626-66-2-2-622-220000000000i2i2−i2−i2−i2−i2i2i2000000-66-6226-2-22-20000000000−i2−i2i2i2i2i2−i2−i2000000
χ636-66-2-2-622-220000000000−i2−i2i2i2i2i2−i2−i2000000-66-6226-2-22-20000000000i2i2−i2−i2−i2−i2i2i2000000
χ646-6-26-22-62-220000000000i2−i2i2−i2−i2i2−i2i2000000-662-62-26-22-20000000000−i2i2−i2i2i2−i2i2−i2000000
χ656-6-26-22-62-220000000000−i2i2−i2i2i2−i2i2−i2000000-662-62-26-22-20000000000i2−i2i2−i2−i2i2−i2i2000000
χ666-6-2-2622-6-2200000000002−2−22−222−2000000-6622-6-2-262-20000000000−222−22−2−22000000
χ676-6-2-2622-6-220000000000−222−22−2−22000000-6622-6-2-262-200000000002−2−22−222−2000000
χ6812-12-4-4-44444-4000000000000000000000000-1212444-4-4-4-44000000000000000000000000

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