Finite Group Databasebeta

← Group #72275065

Character table — Group #72275065

Order 2304.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size112222244666688888121212121212161616161616161618182424242424242424323232323232323232323232323232323232323236363636484872729696969696969696
order12236662222242666622446633666666242444661212336666666666666666662244121244666612121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111111111−1+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−i3211111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ3111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111111111−1−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+i3211111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ41111111111-11-11111111111111111111-1-1-1-111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1
χ51111111111-11-111111111111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1-1-1111111−1+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−i32-1-1-1-111-1-11−i321−i321+i321+i321−i321−i321+i321+i32
χ61111111111-11-111111111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1-1-1111111−1−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+i32-1-1-1-111-1-11+i321+i321−i321−i321+i321+i321−i321−i32
χ71111111-1-11111-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111111-11-1111-1-1-1-1111-1-1-1-11111-1-1-1-11-11-11-11-1
χ81111111-1-11111-1-1-1-1-1111111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i3211-1-1-1-11111−1+i32−1−i32−1+i321−i32−1−i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321111-1-1-1-1−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32
χ91111111-1-11111-1-1-1-1-1111111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i3211-1-1-1-11111−1−i32−1+i32−1−i321+i32−1+i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321111-1-1-1-1−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32
χ101111111-1-11-11-1-1-1-1-1-111111111-1-1-1-111-1-111-1-11111111-11-1111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-11-11-11-11
χ111111111-1-11-11-1-1-1-1-1-1111111−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32-1-111-1-11111−1+i32−1−i32−1+i321−i32−1−i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32-1-1-1-1-1-1111−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i32
χ121111111-1-11-11-1-1-1-1-1-1111111−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32-1-111-1-11111−1−i32−1+i32−1−i321+i32−1+i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32-1-1-1-1-1-1111+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32
χ1311-11-1-1111-111-1-111-1-11-11-1-11111111111-11-11-11-11-111-1-1-1-11-1-111-1-11-1-111-1-11-11-11-11-11111-1-1-1-1
χ1411-11-1-1111-111-1-111-1-11-11-1-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321-11-11-11-11-1−1+i32−1−i321−i321−i321+i321+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321-11-11-11-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ1511-11-1-1111-111-1-111-1-11-11-1-11−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-11-11-11-11-1−1−i32−1+i321+i321+i321−i321−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321-11-11-11-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ1611-11-1-1111-1-111-111-1-11-11-1-1111111111-11-111-11-11-111-1-1-1-11-1-111-1-11-1-111-1-1-11-111-1-11-1-1-1-11111
χ1711-11-1-1111-1-111-111-1-11-11-1-11−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-11-111-11-11-1−1+i32−1−i321−i321−i321+i321+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32-11-111-1-111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ1811-11-1-1111-1-111-111-1-11-11-1-11−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-11-111-11-11-1−1−i32−1+i321+i321+i321−i321−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32-11-111-1-111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ1911-11-1-11-1-1-111-11-1-1111-11-1-1111-1-1-1-1111-1-11-111-11-111-11-111-1-1-1-1111-1-1-1-1111-11-1-11-111-11-1-11-11
χ2011-11-1-11-1-1-111-11-1-1111-11-1-11−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321-1-11-111-11-1−1+i32−1−i321−i32−1+i321+i32−1−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i321+i321+i321+i321+i32−1−i32−1−i321-11-1-11-11−1+i321−i32−1−i321+i321−i32−1+i321+i32−1−i32
χ2111-11-1-11-1-1-111-11-1-1111-11-1-11−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321-1-11-111-11-1−1−i32−1+i321+i32−1−i321−i32−1+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i321−i321−i321−i321−i32−1+i32−1+i321-11-1-11-11−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i32
χ2211-11-1-11-1-1-1-1111-1-1111-11-1-1111-1-1-1-111-111-1-111-11-111-11-111-1-1-1-1111-1-1-1-111-11-11-111-1-11-111-11-1
χ2311-11-1-11-1-1-1-1111-1-1111-11-1-11−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32-111-1-111-11-1−1+i32−1−i321−i32−1+i321+i32−1−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32-11-11-111-11−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i32
χ2411-11-1-11-1-1-1-1111-1-1111-11-1-11−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i32-111-1-111-11-1−1−i32−1+i321+i32−1−i321−i32−1+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32-11-11-111-11+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i32
χ25222-1-1-1-12220202-1-1-1-12222-1-122222222000022-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-10000000000
χ26222-1-1-1-12220202-1-1-1-12222-1-1−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i3000022-1-1-1-11−i321+i32−1+i3−1+i3−1−i3−1−i31−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i320000-1-10000000000
χ27222-1-1-1-12220202-1-1-1-12222-1-1−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3000022-1-1-1-11+i321−i32−1−i3−1−i3−1+i3−1+i31+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i320000-1-10000000000
χ28222-1-1-1-1-2-22020-211112222-1-122-2-2-2-2220000-2-2-1-1-1-1-1-12-22-2-1-1-11111-1-1-111110000110000000000
χ29222-1-1-1-1-2-22020-211112222-1-1−1+i3−1−i31−i31−i31+i31+i3−1+i3−1−i30000-2-2-1-1-1-11−i321+i32−1+i31−i3−1−i31+i31−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i320000110000000000
χ30222-1-1-1-1-2-22020-211112222-1-1−1−i3−1+i31+i31+i31−i31−i3−1−i3−1+i30000-2-2-1-1-1-11+i321−i32−1−i31+i3−1+i31−i31+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i320000110000000000
χ3122-2-111-122-2020-2-1-1112-22-21-12222222200002-2-11-11-1-1-2-2-2-2-111-1-111-111-1-1110000-110000000000
χ3222-2-111-122-2020-2-1-1112-22-21-1−1+i3−1−i3−1+i3−1+i3−1−i3−1−i3−1+i3−1−i300002-2-11-111−i321+i321−i31−i31+i31+i31−i32−1+i32−1+i321−i321−i32−1+i32−1+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i320000-110000000000
χ3322-2-111-122-2020-2-1-1112-22-21-1−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i300002-2-11-111+i321−i321+i31+i31−i31−i31+i32−1−i32−1−i321+i321+i32−1−i32−1−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i320000-110000000000
χ3422-2-111-1-2-2-2020211-1-12-22-21-122-2-2-2-2220000-22-11-11-1-1-22-22-11111-1-1-11111-1-100001-10000000000
χ3522-2-111-1-2-2-2020211-1-12-22-21-1−1+i3−1−i31−i31−i31+i31+i3−1+i3−1−i30000-22-11-111−i321+i321−i3−1+i31+i3−1−i31−i32−1+i32−1+i32−1+i32−1+i321−i321−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i3200001-10000000000
χ3622-2-111-1-2-2-2020211-1-12-22-21-1−1−i3−1+i31+i31+i31−i31−i3−1−i3−1+i30000-22-11-111+i321−i321+i3−1−i31−i3−1+i31+i32−1−i32−1−i32−1−i32−1−i321+i321+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i3200001-10000000000
χ37333333333333333333-1-1-1-133000000003333-1-1-1-1-1-100000000000000000000-1-1-1-1-1-1-1-100000000
χ383333333333-33-333333-1-1-1-13300000000-3-3-3-3-1-1-1-1-1-1000000000000000000001111-1-11100000000
χ393333333-3-33333-3-3-3-3-3-1-1-1-1330000000033-3-311-1-1-1-100000000000000000000-1-1-1-1111100000000
χ403333333-3-33-33-3-3-3-3-3-3-1-1-1-13300000000-3-33311-1-1-1-100000000000000000000111111-1-100000000
χ4133-33-3-3333-333-3-333-3-3-11-11-33000000003-33-3-11-11-1100000000000000000000-11-11-11-1100000000
χ4233-33-3-3333-3-333-333-3-3-11-11-3300000000-33-33-11-11-11000000000000000000001-11-1-111-100000000
χ4333-33-3-33-3-3-333-33-3-333-11-11-33000000003-3-331-1-11-1100000000000000000000-11-111-11-100000000
χ4433-33-3-33-3-3-3-3333-3-333-11-11-3300000000-333-31-1-11-11000000000000000000001-11-11-1-1100000000
χ45666666600-26-260000022-2-2-2-200000000-2-2000022-2-2000000000000000000002-2-22000000000000
χ46666666600-26-2600000-2-222-2-200000000-2-20000-2-22200000000000000000000-222-2000000000000
χ47666666600-2-6-2-60000022-2-2-2-20000000022000022-2-200000000000000000000-222-2000000000000
χ48666666600-2-6-2-600000-2-222-2-200000000220000-2-222000000000000000000002-2-22000000000000
χ49666-3-3-3-36660606-3-3-3-3-2-2-2-2-3-3000000000000-2-21111000000000000000000000000110000000000
χ50666-3-3-3-3-6-66060-63333-2-2-2-2-3-3000000000000221111000000000000000000000000-1-10000000000
χ5166-66-6-660026-2-6000002-2-222-200000000-2200002-2-220000000000000000000022-2-2000000000000
χ5266-66-6-660026-2-600000-222-22-200000000-220000-222-200000000000000000000-2-222000000000000
χ5366-66-6-66002-6-26000002-2-222-2000000002-200002-2-2200000000000000000000-2-222000000000000
χ5466-66-6-66002-6-2600000-222-22-2000000002-20000-222-20000000000000000000022-2-2000000000000
χ5566-6-333-366-6060-6-3-333-22-223-3000000000000-221-11-10000000000000000000000001-10000000000
χ5666-6-333-3-6-6-6060633-3-3-22-223-30000000000002-21-11-1000000000000000000000000-110000000000
χ578-80800-84-4000004-400000000222-22-2-2-20000000000220000-2002-200-2002-2000000000000000000
χ588-80800-84-4000004-400000000−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i30000000000−1+i3−1−i300001−i300−1+i31−i3001+i300−1−i31+i3000000000000000000
χ598-80800-84-4000004-400000000−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i30000000000−1−i3−1+i300001+i300−1−i31+i3001−i300−1+i31−i3000000000000000000
χ608-80800-8-4400000-440000000022-22-22-2-20000000000220000-200-2200-200-22000000000000000000
χ618-80800-8-4400000-4400000000−1+i3−1−i31−i3−1+i31+i3−1−i31−i31+i30000000000−1+i3−1−i300001−i3001−i3−1+i3001+i3001+i3−1−i3000000000000000000
χ628-80800-8-4400000-4400000000−1−i3−1+i31+i3−1−i31−i3−1+i31+i31−i30000000000−1−i3−1+i300001+i3001+i3−1−i3001−i3001−i3−1+i3000000000000000000
χ638-80-44i3−4i344-400000-222i3−2i3000000222-22-2-2-20000000000-1-100001i3−i3-11i3−i31i3−i3-11i3−i30000000000000000
χ648-80-44i3−4i344-400000-222i3−2i3000000−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i300000000001−i321+i320000−1+i32−3−i323+i321−i32−1+i32−3−i323+i32−1−i323−i32−3+i321+i32−1−i323−i32−3+i320000000000000000
χ658-80-44i3−4i344-400000-222i3−2i3000000−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i300000000001+i321−i320000−1−i323−i32−3+i321+i32−1−i323−i32−3+i32−1+i32−3−i323+i321−i32−1+i32−3−i323+i320000000000000000
χ668-80-44i3−4i34-44000002-2−2i32i300000022-22-22-2-20000000000-1-100001i3−i31-1−i3i31i3−i31-1−i3i30000000000000000
χ678-80-44i3−4i34-44000002-2−2i32i3000000−1+i3−1−i31−i3−1+i31+i3−1−i31−i31+i300000000001−i321+i320000−1+i32−3−i323+i32−1+i321−i323+i32−3−i32−1−i323−i32−3+i32−1−i321+i32−3+i323−i320000000000000000
χ688-80-44i3−4i34-44000002-2−2i32i3000000−1−i3−1+i31+i3−1−i31−i3−1+i31+i31−i300000000001+i321−i320000−1−i323−i32−3+i32−1−i321+i32−3+i323−i32−1+i32−3−i323+i32−1+i321−i323+i32−3−i320000000000000000
χ698-80-4−4i34i344-400000-22−2i32i3000000222-22-2-2-20000000000-1-100001−i3i3-11−i3i31−i3i3-11−i3i30000000000000000
χ708-80-4−4i34i344-400000-22−2i32i3000000−1+i3−1−i3−1+i31−i3−1−i31+i31−i31+i300000000001−i321+i320000−1+i323+i32−3−i321−i32−1+i323+i32−3−i32−1−i32−3+i323−i321+i32−1−i32−3+i323−i320000000000000000
χ718-80-4−4i34i344-400000-22−2i32i3000000−1−i3−1+i3−1−i31+i3−1+i31−i31+i31−i300000000001+i321−i320000−1−i32−3+i323−i321+i32−1−i32−3+i323−i32−1+i323+i32−3−i321−i32−1+i323+i32−3−i320000000000000000
χ728-80-4−4i34i34-44000002-22i3−2i300000022-22-22-2-20000000000-1-100001−i3i31-1i3−i31−i3i31-1i3−i30000000000000000
χ738-80-4−4i34i34-44000002-22i3−2i3000000−1+i3−1−i31−i3−1+i31+i3−1−i31−i31+i300000000001−i321+i320000−1+i323+i32−3−i32−1+i321−i32−3−i323+i32−1−i32−3+i323−i32−1−i321+i323−i32−3+i320000000000000000
χ748-80-4−4i34i34-44000002-22i3−2i3000000−1−i3−1+i31+i3−1−i31−i3−1+i31+i31−i300000000001+i321−i320000−1−i32−3+i323−i32−1−i321+i323−i32−3+i32−1+i323+i32−3−i32−1+i321−i32−3−i323+i320000000000000000
χ75121212-6-6-6-600-40-400000044-4-42200000000000000-2-222000000000000000000000000000000000000
χ76121212-6-6-6-600-40-4000000-4-444220000000000000022-2-2000000000000000000000000000000000000
χ771212-12-666-60040-40000004-4-44-2200000000000000-222-2000000000000000000000000000000000000
χ781212-12-666-60040-4000000-444-4-22000000000000002-2-22000000000000000000000000000000000000

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