Finite Group Databasebeta

← Group #13147031

Character table — Group #13147031

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111111122222266666666666666666666121212121212121212121212242424242424242424242424242424242424242424242424363636363636363636363636363636363636363636363636
order123344661212121288242424242346668812121212242424242424242466612121224242424242433366612121212121224242424242424242424242424446688881212121212122424242424242424
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
χ3111111111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111
χ4111111111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1
χ51111-1-111-1-1-1-1i−iii−i−i-1111-1-1i−i-1-111ii−i−iii−i−i-1-1-1111iii−i−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i1-1i−i11i−i1-1-1-1ii−i−iii−i−i11-1-1
χ61111-1-111-1-1-1-1i−iii−i−i-1111-1-1i−i-1-111ii−i−iii−i−i-1-1-1111iii−i−i−i111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i-11−ii-1-1−ii-1111−i−iii−i−iii-1-111
χ71111-1-111-1-1-1-1−ii−i−iii-1111-1-1−ii-1-111−i−iii−i−iii-1-1-1111−i−i−iiii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii1-1−ii11−ii1-1-1-1−i−iii−i−iii11-1-1
χ81111-1-111-1-1-1-1−ii−i−iii-1111-1-1−ii-1-111−i−iii−i−iii-1-1-1111−i−i−iiii111111-1-1-1-1-1-1−i−i−i−i−i−iiiiiii-11i−i-1-1i−i-1111ii−i−iii−i−i-1-111
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
χ102222222222222222222-12-12222-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-1000000000000000000000000
χ112222222222222222222-12-12222-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-1-122-1-1-1-122-1-1-1-122-1-1000000000000000000000000
χ122222222222222222222-12-12222-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-1-12-1-1-1-122-1-1-1-122-1-1-1-122000000000000000000000000
χ13222222222222-2-2-2-2-2-2222222-2-22222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111000000000000000000000000
χ14222222222222-2-2-2-2-2-22-12-122-2-2-1-122-2-2-2-21111-1-1-1-1-1-11111112-1-12-1-122-1-1-1-1-2-21111-2-21111000000000000000000000000
χ15222222222222-2-2-2-2-2-22-12-122-2-2-1-122-2-2-2-21111-1-1-1-1-1-1111111-12-1-12-1-1-122-1-111-2-21111-2-211000000000000000000000000
χ16222222222222-2-2-2-2-2-22-12-122-2-2-1-122-2-2-2-21111-1-1-1-1-1-1111111-1-12-1-12-1-1-1-1221111-2-21111-2-2000000000000000000000000
χ172222-2-222-2-2-2-22i−2i2i2i−2i−2i-2222-2-22i−2i-2-2222i2i−2i−2i2i2i−2i−2i-2-2-22222i2i2i−2i−2i−2i-1-1-1-1-1-1111111−i−i−i−i−i−iiiiiii000000000000000000000000
χ182222-2-222-2-2-2-22i−2i2i2i−2i−2i-2-12-1-2-22i−2i11222i2i−2i−2i−i−iii111-1-1-1−i−i−iiii2-1-12-1-1-2-211112i2i−i−i−i−i−2i−2iiiii000000000000000000000000
χ192222-2-222-2-2-2-22i−2i2i2i−2i−2i-2-12-1-2-22i−2i11222i2i−2i−2i−i−iii111-1-1-1−i−i−iiii-12-1-12-111-2-211−i−i2i2i−i−iii−2i−2iii000000000000000000000000
χ202222-2-222-2-2-2-22i−2i2i2i−2i−2i-2-12-1-2-22i−2i11222i2i−2i−2i−i−iii111-1-1-1−i−i−iiii-1-12-1-121111-2-2−i−i−i−i2i2iiiii−2i−2i000000000000000000000000
χ212222-2-222-2-2-2-2−2i2i−2i−2i2i2i-2222-2-2−2i2i-2-222−2i−2i2i2i−2i−2i2i2i-2-2-2222−2i−2i−2i2i2i2i-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i000000000000000000000000
χ222222-2-222-2-2-2-2−2i2i−2i−2i2i2i-2-12-1-2-2−2i2i1122−2i−2i2i2iii−i−i111-1-1-1iii−i−i−i2-1-12-1-1-2-21111−2i−2iiiii2i2i−i−i−i−i000000000000000000000000
χ232222-2-222-2-2-2-2−2i2i−2i−2i2i2i-2-12-1-2-2−2i2i1122−2i−2i2i2iii−i−i111-1-1-1iii−i−i−i-12-1-12-111-2-211ii−2i−2iii−i−i2i2i−i−i000000000000000000000000
χ242222-2-222-2-2-2-2−2i2i−2i−2i2i2i-2-12-1-2-2−2i2i1122−2i−2i2i2iii−i−i111-1-1-1iii−i−i−i-1-12-1-121111-2-2iiii−2i−2i−i−i−i−i2i2i000000000000000000000000
χ25333333333333333333-13-13-1-1-1-133-1-1-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000011-1-11111-1-111-1-1-1-11111-1-1-1-1
χ26333333333333333333-13-13-1-1-1-133-1-1-1-1-1-13333-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-1-111-1-1-1-111-1-11111-1-1-1-11111
χ27333333333333-3-3-3-3-3-3-13-13-1-11133-1-11111-3-3-3-3-1-1-1-1-1-1111111000000000000000000000000111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ28333333333333-3-3-3-3-3-3-13-13-1-11133-1-11111-3-3-3-3-1-1-1-1-1-1111111000000000000000000000000-1-1-1-1-1-11111-1-1-1-1-1-111111111
χ293333-3-333-3-3-3-33i−3i3i3i−3i−3i13-1311−ii-3-3-1-1−i−iii3i3i−3i−3i111-1-1-1−i−i−iiii0000000000000000000000001-1−ii11i−i-11-1-1−i−iiiii−i−i-1-111
χ303333-3-333-3-3-3-33i−3i3i3i−3i−3i13-1311−ii-3-3-1-1−i−iii3i3i−3i−3i111-1-1-1−i−i−iiii000000000000000000000000-11i−i-1-1−ii1-111ii−i−i−i−iii11-1-1
χ313333-3-333-3-3-3-3−3i3i−3i−3i3i3i13-1311i−i-3-3-1-1ii−i−i−3i−3i3i3i111-1-1-1iii−i−i−i0000000000000000000000001-1i−i11−ii-11-1-1ii−i−i−i−iii-1-111
χ323333-3-333-3-3-3-3−3i3i−3i−3i3i3i13-1311i−i-3-3-1-1ii−i−i−3i−3i3i3i111-1-1-1iii−i−i−i000000000000000000000000-11−ii-1-1i−i1-111−i−iiiii−i−i11-1-1
χ3333−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3−3i32−3+3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i323030−3−3i32−3+3i323300−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3200000000000000000000000000000000000000001111−1−i32−1+i321111−1−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+3i323030−3−3i32−3+3i323300−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i320000000000000000000000000000000000000000-1-1-1-11+i321−i32-1-1-1-11+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+3i32-10-101+i321−i32-1-1001+i321−i321+i321−i321+i321−i3200002−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i300000000000000000000000011-1-1−1−i32−1+i3211-1-1−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+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+3i32-10-101+i321−i32-1-1001+i321−i321+i321−i321+i321−i3200002−1−i3−1+i32−1−i3−1+i32−1−i3−1+i32−1−i3−1+i3000000000000000000000000-1-1111+i321−i32-1-1111+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−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+3i323−3i323030−3−3i32−3+3i32-3-300−3−3i32−3+3i323+3i323−3i323+3i323−3i32000000000000000000000000000000000000000011-1-1−1−i32−1+i32-1-111−1−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+3i323−3i323030−3−3i32−3+3i32-3-300−3−3i32−3+3i323+3i323−3i323+3i323−3i320000000000000000000000000000000000000000-1-1111+i321−i3211-1-11+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+3i323−3i32-10-101+i321−i3211001+i321−i32−1−i32−1+i32−1−i32−1+i3200002−1−i3−1+i32−1−i3−1+i3-21+i31−i3-21+i31−i30000000000000000000000001111−1−i32−1+i32-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−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+3i323−3i32-10-101+i321−i3211001+i321−i32−1−i32−1+i32−1−i32−1+i3200002−1−i3−1+i32−1−i3−1+i3-21+i31−i3-21+i31−i3000000000000000000000000-1-1-1-11+i321−i3211111+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ4133−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i323i−3i3ζ223ζ14−3ζ22−3ζ1410-10−1−i32−1+i32−ii001+i321−i32−ζ22−ζ14ζ22ζ140000-21+i31−i32−1−i3−1+i32i2ζ222ζ14−2i−2ζ22−2ζ140000000000000000000000001-1−ii−1−i32−1+i32i−i-111+i321−i32−ζ22−ζ14ζ22ζ14ζ22ζ14−ζ22−ζ141+i321−i32−1−i32−1+i32
χ4233−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i323i−3i3ζ223ζ14−3ζ22−3ζ1410-10−1−i32−1+i32−ii001+i321−i32−ζ22−ζ14ζ22ζ140000-21+i31−i32−1−i3−1+i32i2ζ222ζ14−2i−2ζ22−2ζ14000000000000000000000000-11i−i1+i321−i32−ii1-1−1−i32−1+i32ζ22ζ14−ζ22−ζ14−ζ22−ζ14ζ22ζ14−1−i32−1+i321+i321−i32
χ4333−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i323i−3i3ζ223ζ14−3ζ22−3ζ14-30303+3i323−3i323i−3i00−3−3i32−3+3i323ζ223ζ14−3ζ22−3ζ1400000000000000000000000000000000000000001-1i−i−1−i32−1+i32i−i1-11+i321−i32ζ22ζ14−ζ22−ζ14ζ22ζ14−ζ22−ζ14−1−i32−1+i321+i321−i32
χ4433−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i323i−3i3ζ223ζ14−3ζ22−3ζ14-30303+3i323−3i323i−3i00−3−3i32−3+3i323ζ223ζ14−3ζ22−3ζ140000000000000000000000000000000000000000-11−ii1+i321−i32−ii-11−1−i32−1+i32−ζ22−ζ14ζ22ζ14−ζ22−ζ14ζ22ζ141+i321−i32−1−i32−1+i32
χ4533−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i32−3i3i−3ζ22−3ζ143ζ223ζ1410-10−1−i32−1+i32i−i001+i321−i32ζ22ζ14−ζ22−ζ140000-21+i31−i32−1−i3−1+i3−2i−2ζ22−2ζ142i2ζ222ζ140000000000000000000000001-1i−i−1−i32−1+i32−ii-111+i321−i32ζ22ζ14−ζ22−ζ14−ζ22−ζ14ζ22ζ141+i321−i32−1−i32−1+i32
χ4633−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i32−3i3i−3ζ22−3ζ143ζ223ζ1410-10−1−i32−1+i32i−i001+i321−i32ζ22ζ14−ζ22−ζ140000-21+i31−i32−1−i3−1+i3−2i−2ζ22−2ζ142i2ζ222ζ14000000000000000000000000-11−ii1+i321−i32i−i1-1−1−i32−1+i32−ζ22−ζ14ζ22ζ14ζ22ζ14−ζ22−ζ14−1−i32−1+i321+i321−i32
χ4733−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i32−3i3i−3ζ22−3ζ143ζ223ζ14-30303+3i323−3i32−3i3i00−3−3i32−3+3i32−3ζ22−3ζ143ζ223ζ1400000000000000000000000000000000000000001-1−ii−1−i32−1+i32−ii1-11+i321−i32−ζ22−ζ14ζ22ζ14−ζ22−ζ14ζ22ζ14−1−i32−1+i321+i321−i32
χ4833−3−3i32−3+3i32-3-3−3−3i32−3+3i323+3i323+3i323−3i323−3i32−3i3i−3ζ22−3ζ143ζ223ζ14-30303+3i323−3i32−3i3i00−3−3i32−3+3i32−3ζ22−3ζ143ζ223ζ140000000000000000000000000000000000000000-11i−i1+i321−i32i−i-11−1−i32−1+i32ζ22ζ14−ζ22−ζ14ζ22ζ14−ζ22−ζ141+i321−i32−1−i32−1+i32
χ4933−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3+3i32−3−3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i323030−3+3i32−3−3i323300−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3200000000000000000000000000000000000000001111−1+i32−1−i321111−1+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+3i32−3−3i323030−3+3i32−3−3i323300−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i320000000000000000000000000000000000000000-1-1-1-11−i321+i32-1-1-1-11−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+3i32−3−3i32-10-101−i321+i32-1-1001−i321+i321−i321+i321−i321+i3200002−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i300000000000000000000000011-1-1−1+i32−1−i3211-1-1−1+i32−1−i321−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−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+3i32−3−3i32-10-101−i321+i32-1-1001−i321+i321−i321+i321−i321+i3200002−1+i3−1−i32−1+i3−1−i32−1+i3−1−i32−1+i3−1−i3000000000000000000000000-1-1111−i321+i32-1-1111−i321+i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+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+3i323030−3+3i32−3−3i32-3-300−3+3i32−3−3i323−3i323+3i323−3i323+3i32000000000000000000000000000000000000000011-1-1−1+i32−1−i32-1-111−1+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+3i323030−3+3i32−3−3i32-3-300−3+3i32−3−3i323−3i323+3i323−3i323+3i320000000000000000000000000000000000000000-1-1111−i321+i3211-1-11−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+3i32-10-101−i321+i3211001−i321+i32−1+i32−1−i32−1+i32−1−i3200002−1+i3−1−i32−1+i3−1−i3-21−i31+i3-21−i31+i30000000000000000000000001111−1+i32−1−i32-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321−i321+i321−i321+i32
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.