Finite Group Databasebeta

← Group #11919850

Character table — Group #11919850

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54
size111333444666666121212121212121212121212121212121212121212121212121212646464646464646464646464
order133266266441212121222444444466661212121212121212121212121212333333666666
χ1111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ3111111111111111111111111111111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ4111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1
χ5111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321+i321+i321+i321−i321−i321−i32
χ6111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11111111111-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−i321−i321−i321+i321+i321+i32
χ71−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32111111111−1−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−i32−1+i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i321−1−i32−1+i32
χ81−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32111111111−1−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−i32−1+i32−1+i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32
χ91−1−i32−1+i321−1−i32−1+i321−1−i32−1+i3211−1−i32−1−i32−1+i32−1+i32111111111−1−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−i32−1+i32−1+i32−1+i321−1−i32−1−i32−1+i321−1+i321−1−i32−1−i32−1+i321
χ101−1−i32−1+i321−1−i32−1+i32-11+i321−i32-1-11+i321+i321−i321−i32-1-111111-1-11+i321+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i321−1−i32−1+i321−1−i32−1+i32-11+i321−i32-11+i321−i32
χ111−1−i32−1+i321−1−i32−1+i32-11+i321−i32-1-11+i321+i321−i321−i32-1-111111-1-11+i321+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1+i321−1+i321−1−i321+i321−i32-11−i32-11+i32
χ121−1−i32−1+i321−1−i32−1+i32-11+i321−i32-1-11+i321+i321−i321−i32-1-111111-1-11+i321+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i32−1+i321−1−i32−1−i32−1+i3211−i32-11+i321+i321−i32-1
χ131−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32111111111−1+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+i32−1−i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i321−1+i32−1−i32
χ141−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32111111111−1+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+i32−1−i32−1−i32−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i321
χ151−1+i32−1−i321−1+i32−1−i321−1+i32−1−i3211−1+i32−1+i32−1−i32−1−i32111111111−1+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+i32−1−i32−1−i32−1+i32−1−i321−1−i321−1+i32−1+i32−1−i321−1−i321−1+i32
χ161−1+i32−1−i321−1+i32−1−i32-11−i321+i32-1-11−i321−i321+i321+i32-1-111111-1-11−i321−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i321−1+i32−1−i321−1+i32−1−i32-11−i321+i32-11−i321+i32
χ171−1+i32−1−i321−1+i32−1−i32-11−i321+i32-1-11−i321−i321+i321+i32-1-111111-1-11−i321−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i32−1−i321−1+i32−1+i32−1−i3211+i32-11−i321−i321+i32-1
χ181−1+i32−1−i321−1+i32−1−i32-11−i321+i32-1-11−i321−i321+i321+i32-1-111111-1-11−i321−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−1−i321−1+i321−i321+i32-11+i32-11−i32
χ19333333333333333-1-13-1-1-1-1-1-1-1-1-1-13-1-1-1-13-1-1-1-1-1-1-1-1000000000000
χ20333333333-1-1-1-1-1-13-1-13-1-1-1-1-13-13-1-13-1-1-1-13-1-1-1-1-1-1-1000000000000
χ21333333333-1-1-1-1-1-1-13-1-13-1-1-1-1-13-13-1-13-1-1-1-13-1-1-1-1-1-1000000000000
χ22333333333-1-1-1-1-1-1-1-1-1-1-13-13-1-1-1-1-1-1-1-13-1-1-1-13-13-13-1000000000000
χ23333333333-1-1-1-1-1-1-1-1-1-1-1-13-13-1-1-1-1-1-1-1-13-1-1-1-13-13-13000000000000
χ24333333-3-3-311111111-1-1-13-1-311111-1-1-13-1-1-1-13-1-31-31000000000000
χ25333333-3-3-311111111-1-1-1-131-31111-1-1-1-13-1-1-1-131-31-3000000000000
χ26333333-3-3-31111111-3-1-13-1-1111-31-3-1-13-1-1-1-13-1-11111000000000000
χ27333333-3-3-3111111-31-13-1-1-111-31-31-13-1-1-1-13-1-1-11111000000000000
χ28333333-3-3-3-3-3-3-3-3-3113-1-1-1-11111113-1-1-1-13-1-1-1-11111000000000000
χ293−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i3233−3−3i32−3−3i32−3+3i32−3+3i32-1-13-1-1-1-1-1-11+i321+i321−i321−i32−3−3i321+i321+i321+i321+i32−3+3i321−i321−i321−i321−i321+i321+i321−i321−i32000000000000
χ303−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i32-1-11+i321+i321−i321−i323-1-13-1-1-1-1-1−3−3i321+i32−3+3i321−i321+i32−3−3i321+i321+i321+i321−i32−3+3i321−i321−i321−i321+i321+i321−i321−i32000000000000
χ313−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i32-1-11+i321+i321−i321−i32-13-1-13-1-1-1-11+i32−3−3i321−i32−3+3i321+i321+i32−3−3i321+i321+i321−i321−i32−3+3i321−i321−i321+i321+i321−i321−i32000000000000
χ323−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i32-1-11+i321+i321−i321−i32-1-1-1-1-13-13-11+i321+i321−i321−i321+i321+i321+i32−3−3i321+i321−i321−i321−i32−3+3i321−i32−3−3i321+i32−3+3i321−i32000000000000
χ333−3−3i32−3+3i323−3−3i32−3+3i323−3−3i32−3+3i32-1-11+i321+i321−i321−i32-1-1-1-1-1-13-131+i321+i321−i321−i321+i321+i321+i321+i32−3−3i321−i321−i321−i321−i32−3+3i321+i32−3−3i321−i32−3+3i32000000000000
χ343−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i3211−1−i32−1−i32−1+i32−1+i3211-1-1-13-1-31−1−i32−1−i32−1+i32−1+i321+i321+i321+i32−3−3i321+i321−i321−i321−i32−3+3i321−i323+3i32−1−i323−3i32−1+i32000000000000
χ353−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i3211−1−i32−1−i32−1+i32−1+i3211-1-1-1-131-3−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i32−3−3i321−i321−i321−i321−i32−3+3i32−1−i323+3i32−1+i323−3i32000000000000
χ363−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i3211−1−i32−1−i32−1+i32−1+i321-3-1-13-1-111−1−i323+3i32−1+i323−3i321+i321+i32−3−3i321+i321+i321−i321−i32−3+3i321−i321−i32−1−i32−1−i32−1+i32−1+i32000000000000
χ373−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i3211−1−i32−1−i32−1+i32−1+i32-31-13-1-1-1113+3i32−1−i323−3i32−1+i321+i32−3−3i321+i321+i321+i321−i32−3+3i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i32000000000000
χ383−3−3i32−3+3i323−3−3i32−3+3i32-33+3i323−3i32-3-33+3i323+3i323−3i323−3i32113-1-1-1-111−1−i32−1−i32−1+i32−1+i32−3−3i321+i321+i321+i321+i32−3+3i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i32000000000000
χ393−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i3233−3+3i32−3+3i32−3−3i32−3−3i32-1-13-1-1-1-1-1-11−i321−i321+i321+i32−3+3i321−i321−i321−i321−i32−3−3i321+i321+i321+i321+i321−i321−i321+i321+i32000000000000
χ403−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32-1-11−i321−i321+i321+i323-1-13-1-1-1-1-1−3+3i321−i32−3−3i321+i321−i32−3+3i321−i321−i321−i321+i32−3−3i321+i321+i321+i321−i321−i321+i321+i32000000000000
χ413−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32-1-11−i321−i321+i321+i32-13-1-13-1-1-1-11−i32−3+3i321+i32−3−3i321−i321−i32−3+3i321−i321−i321+i321+i32−3−3i321+i321+i321−i321−i321+i321+i32000000000000
χ423−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32-1-11−i321−i321+i321+i32-1-1-1-1-13-13-11−i321−i321+i321+i321−i321−i321−i32−3+3i321−i321+i321+i321+i32−3−3i321+i32−3+3i321−i32−3−3i321+i32000000000000
χ433−3+3i32−3−3i323−3+3i32−3−3i323−3+3i32−3−3i32-1-11−i321−i321+i321+i32-1-1-1-1-1-13-131−i321−i321+i321+i321−i321−i321−i321−i32−3+3i321+i321+i321+i321+i32−3−3i321−i32−3+3i321+i32−3−3i32000000000000
χ443−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i3211−1+i32−1+i32−1−i32−1−i3211-1-1-13-1-31−1+i32−1+i32−1−i32−1−i321−i321−i321−i32−3+3i321−i321+i321+i321+i32−3−3i321+i323−3i32−1+i323+3i32−1−i32000000000000
χ453−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i3211−1+i32−1+i32−1−i32−1−i3211-1-1-1-131-3−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i32−3+3i321+i321+i321+i321+i32−3−3i32−1+i323−3i32−1−i323+3i32000000000000
χ463−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i3211−1+i32−1+i32−1−i32−1−i321-3-1-13-1-111−1+i323−3i32−1−i323+3i321−i321−i32−3+3i321−i321−i321+i321+i32−3−3i321+i321+i32−1+i32−1+i32−1−i32−1−i32000000000000
χ473−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i3211−1+i32−1+i32−1−i32−1−i32-31-13-1-1-1113−3i32−1+i323+3i32−1−i321−i32−3+3i321−i321−i321−i321+i32−3−3i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i32000000000000
χ483−3+3i32−3−3i323−3+3i32−3−3i32-33−3i323+3i32-3-33−3i323−3i323+3i323+3i32113-1-1-1-111−1+i32−1+i32−1−i32−1−i32−3+3i321−i321−i321−i321−i32−3−3i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i32000000000000
χ49121212-4-4-40004i−4i4i−4i4i−4i000000000000000000000000000000000000000
χ50121212-4-4-4000−4i4i−4i4i−4i4i000000000000000000000000000000000000000
χ5112−6−6i3−6+6i3-42+2i32−2i30004i−4i4ζ11−4ζ114ζ7−4ζ7000000000000000000000000000000000000000
χ5212−6−6i3−6+6i3-42+2i32−2i3000−4i4i−4ζ114ζ11−4ζ74ζ7000000000000000000000000000000000000000
χ5312−6+6i3−6−6i3-42−2i32+2i30004i−4i4ζ7−4ζ74ζ11−4ζ11000000000000000000000000000000000000000
χ5412−6+6i3−6−6i3-42−2i32+2i3000−4i4i−4ζ74ζ7−4ζ114ζ11000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.