Finite Group Databasebeta

← Group #72340988

Character table — Group #72340988

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size113344444466661212121212122424242424242424242424242424242464646464646464646464646464646464
order1222222222444444444422444444444444443366666666666666
χ11111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ3111111111111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ4111111-1-1-1-1111111-1-1-1-1111111-1-1-1-111-1-1-1-111111-1-1-1-1111-1-1-1-1
χ5111111-1-1-1-1111111-1-1-1-1111111-1-1-1-111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ6111111-1-1-1-1111111-1-1-1-1111111-1-1-1-111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ71111-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1111-1-111-1-11-1-111-1-1
χ81111-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1−1−i32−1+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32
χ91111-1-111-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1−1+i32−1−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ101111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-1-111111-1-1-1-1111-1-1-1-111
χ111111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-1-111−1−i32−1+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32
χ121111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-1-111−1+i32−1−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32
χ1333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ143333333333-1-1-1-1-1-1-1-1-1-13-1-1-1-1-1-1-1-1-13-13-13-10000000000000000
χ153333333333-1-1-1-1-1-1-1-1-1-1-13-1-1-1-1-1-1-1-1-13-13-130000000000000000
χ163333333333-1-1-1-1-1-1-1-1-1-1-1-13-13-13-13-1-1-1-1-1-1-10000000000000000
χ173333333333-1-1-1-1-1-1-1-1-1-1-1-1-13-13-13-13-1-1-1-1-1-10000000000000000
χ18333333-3-3-3-3333333-3-3-3-3-1-1-1-1-1-11111-1-111110000000000000000
χ19333333-3-3-3-3-1-1-1-1-1-111113-1-1-1-1-111113-1-31-310000000000000000
χ20333333-3-3-3-3-1-1-1-1-1-11111-13-1-1-1-11111-131-31-30000000000000000
χ21333333-3-3-3-3-1-1-1-1-1-11111-1-13-13-1-31-31-1-111110000000000000000
χ22333333-3-3-3-3-1-1-1-1-1-11111-1-1-13-131-31-3-1-111110000000000000000
χ233333-3-333-3-31111-1-1-1-111113-1-313-1-31-1-1-1-1110000000000000000
χ243333-3-333-3-31111-1-1-1-11111-131-3-131-3-1-1-1-1110000000000000000
χ253333-3-333-3-31111-1-1-1-1111-3-1-111-1-111-13-131-30000000000000000
χ263333-3-333-3-31111-1-1-1-111-31-1-111-1-1113-13-1-310000000000000000
χ273333-3-333-3-3-3-3-3-33333-3-311-1-111-1-111-1-1-1-1110000000000000000
χ283333-3-3-3-3331111-1-111-1-1113-1-31-313-1-1-111-1-10000000000000000
χ293333-3-3-3-3331111-1-111-1-111-131-31-3-13-1-111-1-10000000000000000
χ303333-3-3-3-3331111-1-111-1-11-3-1-11111-1-1-131-3-130000000000000000
χ313333-3-3-3-3331111-1-111-1-1-31-1-11111-1-13-1-313-10000000000000000
χ323333-3-3-3-333-3-3-3-333-3-33311-1-11111-1-1-1-111-1-10000000000000000
χ334-4-444-44-44-40000000000000000000000000011-11-11-11-1-11-11-11-1
χ344-4-444-44-44-400000000000000000000000000−1−i32−1+i321+i32−1−i321+i32−1−i321+i32−1−i321+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32
χ354-4-444-44-44-400000000000000000000000000−1+i32−1−i321−i32−1+i321−i32−1+i321−i32−1+i321−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32
χ364-4-444-4-44-440000000000000000000000000011-11-1-11-11-11-1-11-11
χ374-4-444-4-44-4400000000000000000000000000−1−i32−1+i321+i32−1−i321+i321+i32−1−i321+i32−1−i321−i32−1+i321−i321−i32−1+i321−i32−1+i32
χ384-4-444-4-44-4400000000000000000000000000−1+i32−1−i321−i32−1+i321−i321−i32−1+i321−i32−1+i321+i32−1−i321+i321+i32−1−i321+i32−1−i32
χ394-4-44-444-4-440000000000000000000000000011-1-111-1-11-1-111-1-11
χ404-4-44-444-4-4400000000000000000000000000−1−i32−1+i321+i321+i32−1−i32−1−i321+i321+i32−1−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32
χ414-4-44-444-4-4400000000000000000000000000−1+i32−1−i321−i321−i32−1+i32−1+i321−i321−i32−1+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32
χ424-4-44-44-444-40000000000000000000000000011-1-11-111-1-1-11-111-1
χ434-4-44-44-444-400000000000000000000000000−1−i32−1+i321+i321+i32−1−i321+i32−1−i32−1−i321+i321−i321−i32−1+i321−i32−1+i32−1+i321−i32
χ444-4-44-44-444-400000000000000000000000000−1+i32−1−i321−i321−i32−1+i321−i32−1+i32−1+i321−i321+i321+i32−1−i321+i32−1−i32−1−i321+i32
χ451212-4-400000044-4-4004i−4i4i−4i00000000000000000000000000000000
χ461212-4-400000044-4-400−4i4i−4i4i00000000000000000000000000000000
χ471212-4-4000000-4-444004i−4i−4i4i00000000000000000000000000000000
χ481212-4-4000000-4-44400−4i4i4i−4i00000000000000000000000000000000
χ4912-124-4000000008i−8i4-4000000000000000000000000000000000000
χ5012-124-400000000−8i8i4-4000000000000000000000000000000000000
χ5112-124-40000008i−8i00-44000000000000000000000000000000000000
χ5212-124-4000000−8i8i00-44000000000000000000000000000000000000

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