Finite Group Databasebeta

← Group #13147069

Character table — Group #13147069

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111111122222266666666666666666666121212121212121212121212242424242424242424242424242424242424242424242424363636363636363636363636363636363636363636363636
order12334466121212122466121222344666666612121212121212126666661212121212123336666666661212121212121212121212124444888812121212121212122424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-1-1-1-1111-1-1-1-1-111111-1-111-1-1111-1-1-1111-1-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111-1-1-1-1-1-1-1111-1-1-1-1-111111-1-111-1-1111-1-1-1111-1-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111
χ51111-1-111-1-1-1-11-111-1-1-1-1111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i
χ61111-1-111-1-1-1-11-111-1-1-1-1111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii
χ71111-1-111-1-1-1-1-11-1-1111-111-111-1-11-1-111-1-1-1-111-1-1-1111111-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1111111i−i−iii−i−iiii−i−i−i−iiiii−i−i−i−iii
χ81111-1-111-1-1-1-1-11-1-1111-111-111-1-11-1-111-1-1-1-111-1-1-1111111-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1111111−iii−i−iii−i−i−iiiii−i−i−i−iiiii−i−i
χ922222222222222222222222222222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ1022222222222222222222-12222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-1000000000000000000000000
χ1122222222222222222222-12222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-122-1-1-12-1-1-122-1-1-1-122-1-1000000000000000000000000
χ1222222222222222222222-12222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-1-122-1-12-1-1-1-122-1-1-1-122000000000000000000000000
χ13222222222222-2-2-2-2-2-2-2222-2-2-2-2-222222-2-222-2-2222-2-2-2222-2-2-2-1-1-1111111-1-1-1-1-1-1-1-1-1111111000000000000000000000000
χ14222222222222-2-2-2-2-2-2-22-12-2-2-211-12222-2-2-1-111-1-1-1111-1-1-11112-1-1-2-211112-1-122-1-1-1-1-2-21111000000000000000000000000
χ15222222222222-2-2-2-2-2-2-22-12-2-2-211-12222-2-2-1-111-1-1-1111-1-1-1111-12-111-2-211-12-1-1-122-1-111-2-211000000000000000000000000
χ16222222222222-2-2-2-2-2-2-22-12-2-2-211-12222-2-2-1-111-1-1-1111-1-1-1111-1-121111-2-2-1-12-1-1-1-1221111-2-2000000000000000000000000
χ172222-2-222-2-2-2-22-222-2-2-2-2222-2-2222-2-22222-2-2-2-2-2-2-2-2-2-2222222-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000
χ182222-2-222-2-2-2-22-222-2-2-2-2-122-2-2-1-1-1-2-222221111111111-1-1-1-1-1-12-1-122-1-1-1-12-1-1-2-21111-2-21111000000000000000000000000
χ192222-2-222-2-2-2-22-222-2-2-2-2-122-2-2-1-1-1-2-222221111111111-1-1-1-1-1-1-12-1-1-122-1-1-12-111-2-21111-2-211000000000000000000000000
χ202222-2-222-2-2-2-22-222-2-2-2-2-122-2-2-1-1-1-2-222221111111111-1-1-1-1-1-1-1-12-1-1-1-122-1-121111-2-21111-2-2000000000000000000000000
χ212222-2-222-2-2-2-2-22-2-2222-222-222-2-22-2-222-2-2-2-222-2-2-2222222-2-2-2-1-1-1111111-1-1-1111111-1-1-1-1-1-1000000000000000000000000
χ222222-2-222-2-2-2-2-22-2-2222-2-12-22211-1-2-222-2-211-1-1111-1-1-1-1-1-11112-1-1-2-211112-1-1-2-2111122-1-1-1-1000000000000000000000000
χ232222-2-222-2-2-2-2-22-2-2222-2-12-22211-1-2-222-2-211-1-1111-1-1-1-1-1-1111-12-111-2-211-12-111-2-211-1-122-1-1000000000000000000000000
χ242222-2-222-2-2-2-2-22-2-2222-2-12-22211-1-2-222-2-211-1-1111-1-1-1-1-1-1111-1-121111-2-2-1-121111-2-2-1-1-1-122000000000000000000000000
χ25333333333333333333-1-13-1-1-1-1333-1-1-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000001111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ26333333333333333333-1-13-1-1-1-1333-1-1-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ27333333333333-3-3-3-3-3-31-13-1111-3-33-1-1-1-11133-3-3-1-1-1111-1-1-111100000000000000000000000011-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ28333333333333-3-3-3-3-3-31-13-1111-3-33-1-1-1-11133-3-3-1-1-1111-1-1-1111000000000000000000000000-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ293333-3-333-3-3-3-33-333-3-3113-1-11133311-1-1-1-1-3-3-3-3111111-1-1-1-1-1-1000000000000000000000000i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii
χ303333-3-333-3-3-3-33-333-3-3113-1-11133311-1-1-1-1-3-3-3-3111111-1-1-1-1-1-1000000000000000000000000−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i
χ313333-3-333-3-3-3-3-33-3-333-113-11-1-1-3-3311-1-111-3-333111-1-1-1-1-1-1111000000000000000000000000i−i−ii−iii−iii−i−i−i−iii−i−iiiii−i−i
χ323333-3-333-3-3-3-3-33-3-333-113-11-1-1-3-3311-1-111-3-333111-1-1-1-1-1-1111000000000000000000000000−iii−ii−i−ii−i−iiiii−i−iii−i−i−i−iii
χ3333−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3233033−3−3i32−3+3i32000−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32000000000000000000000000000000000000000011111111−1−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
χ3433−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3233033−3−3i32−3+3i32000−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i320000000000000000000000000000000000000000-1-1-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32
χ3533−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-1-10-1-11+i321−i320001+i321−i321+i321−i321+i321−i3200002−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i30000000000000000000000001111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i32
χ3633−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-1-10-1-11+i321−i320001+i321−i321+i321−i321+i321−i3200002−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3000000000000000000000000-1-1-1-111111+i321−i321+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ3733−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-3-33+3i323−3i323+3i323−3i321-10-11−1−i32−1+i320001+i321−i321+i321−i32−1−i32−1+i3200002−1−i3−1+i3-21+i31−i32−1−i3−1+i3-21+i31−i300000000000000000000000011-1-1-1-111−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ3833−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-3-33+3i323−3i323+3i323−3i321-10-11−1−i32−1+i320001+i321−i321+i321−i32−1−i32−1+i3200002−1−i3−1+i3-21+i31−i32−1−i3−1+i3-21+i31−i3000000000000000000000000-1-11111-1-11+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ3933−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-3-33+3i323−3i323+3i323−3i32-3303-33+3i323−3i32000−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i32000000000000000000000000000000000000000011-1-111-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ4033−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i32-3-33+3i323−3i323+3i323−3i32-3303-33+3i323−3i32000−3−3i32−3+3i32−3−3i32−3+3i323+3i323−3i320000000000000000000000000000000000000000-1-111-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ4133−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i323-3−3−3i32−3+3i323+3i323−3i32110-1-1−1−i32−1+i32000−1−i32−1+i321+i321−i321+i321−i320000-21+i31−i3-21+i31−i32−1−i3−1+i32−1−i3−1+i3000000000000000000000000i−ii−i−ii−iiζ11ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7
χ4233−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i323-3−3−3i32−3+3i323+3i323−3i32110-1-1−1−i32−1+i32000−1−i32−1+i321+i321−i321+i321−i320000-21+i31−i3-21+i31−i32−1−i3−1+i32−1−i3−1+i3000000000000000000000000−ii−iii−ii−i−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7
χ4333−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i323-3−3−3i32−3+3i323+3i323−3i32-3-30333+3i323−3i320003+3i323−3i32−3−3i32−3+3i32−3−3i32−3+3i320000000000000000000000000000000000000000i−ii−ii−ii−iζ11ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7
χ4433−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i323-3−3−3i32−3+3i323+3i323−3i32-3-30333+3i323−3i320003+3i323−3i32−3−3i32−3+3i32−3−3i32−3+3i320000000000000000000000000000000000000000−ii−ii−ii−ii−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7
χ4533−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i32-333+3i323−3i32−3−3i32−3+3i323-303-3−3−3i32−3+3i320003+3i323−3i32−3−3i32−3+3i323+3i323−3i320000000000000000000000000000000000000000i−i−iii−i−iiζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7
χ4633−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i32-333+3i323−3i32−3−3i32−3+3i323-303-3−3−3i32−3+3i320003+3i323−3i32−3−3i32−3+3i323+3i323−3i320000000000000000000000000000000000000000−iii−i−iii−i−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7
χ4733−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i32-333+3i323−3i32−3−3i32−3+3i32-110-111+i321−i32000−1−i32−1+i321+i321−i32−1−i32−1+i320000-21+i31−i32−1−i3−1+i32−1−i3−1+i3-21+i31−i3000000000000000000000000i−i−ii−iii−iζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7
χ4833−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i32-333+3i323−3i32−3−3i32−3+3i32-110-111+i321−i32000−1−i32−1+i321+i321−i32−1−i32−1+i320000-21+i31−i32−1−i3−1+i32−1−i3−1+i3-21+i31−i3000000000000000000000000−iii−ii−i−ii−ζ11−ζ7ζ11ζ7ζ11ζ7−ζ11−ζ7ζ11ζ7−ζ11−ζ7−ζ11−ζ7ζ11ζ7
χ4933−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3233033−3+3i32−3−3i32000−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32000000000000000000000000000000000000000011111111−1+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
χ5033−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3233033−3+3i32−3−3i32000−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i320000000000000000000000000000000000000000-1-1-1-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i32
χ5133−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-1-10-1-11−i321+i320001−i321+i321−i321+i321−i321+i3200002−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i30000000000000000000000001111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321−i321+i321−i321+i32
χ5233−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-1-10-1-11−i321+i320001−i321+i321−i321+i321−i321+i3200002−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3000000000000000000000000-1-1-1-111111−i321+i321−i321+i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32
χ5333−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32-3-33−3i323+3i323−3i323+3i321-10-11−1+i32−1−i320001−i321+i321−i321+i32−1+i32−1−i3200002−1+i3−1−i3-21−i31+i32−1+i3−1−i3-21−i31+i300000000000000000000000011-1-1-1-111−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32
χ5433−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32-3-33−3i323+3i323−3i323+3i321-10-11−1+i32−1−i320001−i321+i321−i321+i32−1+i32−1−i3200002−1+i3−1−i3-21−i31+i32−1+i3−1−i3-21−i31+i3000000000000000000000000-1-11111-1-11−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32
χ5533−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i32-3-33−3i323+3i323−3i323+3i32-3303-33−3i323+3i32000−3+3i32−3−3i32−3+3i32−3−3i323−3i323+3i32000000000000000000000000000000000000000011-1-111-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.