Finite Group Databasebeta

← Group #72229729

Character table — Group #72229729

Order 2688.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91
size112222222444466667777121212121212121212121212121214141414141414141414141414141616282828282828282848484848565656565656565656565656565656565656565656565656112112112112
order1224488884488714141433662828282828285656565656565656661212121224242424242424244412121212242424242828282824668812121616161624242424484848484848484812121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111111111111111111111111-1-111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ511111111111111111−1−i32−1+i32−1−i32−1+i3211111111111111−1−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+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32111111−1−i32−1+i3211−1−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−i32−1+i32−1+i32
χ611111111111111111−1−i32−1+i32−1−i32−1+i3211111111111111−1−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+i3211−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321111-1-11+i321−i32-1-11+i321−i32-1-1-1-11+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ711111111111111111−1−i32−1+i32−1−i32−1+i3211111111111111−1−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−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-111−1−i32−1+i3211−1−i32−1+i32-1-1-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321−i321−i32
χ811111111111111111−1−i32−1+i32−1−i32−1+i3211111111111111−1−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−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-11+i321−i32-1-11+i321−i3211111+i321+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i32
χ911111111111111111−1+i32−1−i32−1+i32−1−i3211111111111111−1+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−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32111111−1+i32−1−i3211−1+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+i32−1−i32−1−i32
χ1011111111111111111−1+i32−1−i32−1+i32−1−i3211111111111111−1+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−i3211−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321111-1-11−i321+i32-1-11−i321+i32-1-1-1-11−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ1111111111111111111−1+i32−1−i32−1+i32−1−i3211111111111111−1+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+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-111−1+i32−1−i3211−1+i32−1−i32-1-1-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321+i321+i32
χ1211111111111111111−1+i32−1−i32−1+i32−1−i3211111111111111−1+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+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-11−i321+i32-1-11−i321+i3211111−i321−i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i32
χ1311111-1-111-1-11-111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-111111-1-1-1-1-111-1-111-1-11111-1-11111-1-1-1-1-1-111-1-111-1-11-11-1
χ1411111-1-111-1-11-111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-111111-1-1-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1111-11-1
χ1511111-1-111-1-11-111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-11-1-1-1-111-1-1-1-1111111-1-111-1-111-1-1-1-1-1-111-1-111-11-11
χ1611111-1-111-1-11-111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-11111-11-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-1111111-1-111-1-1-11-11
χ1711111-1-111-1-11-11111−1−i32−1+i32−1−i32−1+i32-1-1-1-1111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321-11+i321+i321−i321−i32−1−i32−1+i321+i321−i3211-1-111−1−i32−1+i32-1-1−1−i32−1+i3211-1-11+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i321+i32−1+i321−i32
χ1811111-1-111-1-11-11111−1−i32−1+i32−1−i32−1+i32-1-1-1-1111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321-11+i321+i321−i321−i32−1−i32−1+i321+i321−i3211-1-1-1-11+i321−i32111+i321−i32-1-111−1−i32−1−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i321+i32−1+i321−i32
χ1911111-1-111-1-11-11111−1−i32−1+i32−1−i32−1+i32-1-1-1-1111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-111+i321+i321−i321−i32−1−i32−1+i321+i321−i32-1-11111−1−i32−1+i32-1-1−1−i32−1+i32-1-1111+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i32−1−i321−i32−1+i32
χ2011111-1-111-1-11-11111−1−i32−1+i32−1−i32−1+i32-1-1-1-1111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-111+i321+i321−i321−i32−1−i32−1+i321+i321−i32-1-111-1-11+i321−i32111+i321−i3211-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i32−1−i321−i32−1+i32
χ2111111-1-111-1-11-11111−1+i32−1−i32−1+i32−1−i32-1-1-1-1111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321-11−i321−i321+i321+i32−1+i32−1−i321−i321+i3211-1-111−1+i32−1−i32-1-1−1+i32−1−i3211-1-11−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i321−i32−1−i321+i32
χ2211111-1-111-1-11-11111−1+i32−1−i32−1+i32−1−i32-1-1-1-1111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321-11−i321−i321+i321+i32−1+i32−1−i321−i321+i3211-1-1-1-11−i321+i32111−i321+i32-1-111−1+i32−1+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i321−i32−1−i321+i32
χ2311111-1-111-1-11-11111−1+i32−1−i32−1+i32−1−i32-1-1-1-1111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-111−i321−i321+i321+i32−1+i32−1−i321−i321+i32-1-11111−1+i32−1−i32-1-1−1+i32−1−i32-1-1111−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i32−1+i321+i32−1−i32
χ2411111-1-111-1-11-11111−1+i32−1−i32−1+i32−1−i32-1-1-1-1111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32-111−i321−i321+i321+i32−1+i32−1−i321−i321+i32-1-111-1-11−i321+i32111−i321+i3211-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i32−1+i321+i32−1−i32
χ252222222-2-2-2-2-2222222222-2-2-2-222-2-2-2-222222222222222-2-2-2-200-2-2-2-2-2-22200000000000000000000000000000000
χ262222222-2-2-2-2-222222−1−i3−1+i3−1−i3−1+i3-2-2-2-222-2-2-2-22222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i31+i31+i31−i31−i3001+i31+i31−i31−i31+i31−i3−1−i3−1+i300000000000000000000000000000000
χ272222222-2-2-2-2-222222−1+i3−1−i3−1+i3−1−i3-2-2-2-222-2-2-2-22222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i31−i31−i31+i31+i3001−i31−i31+i31+i31−i31+i3−1+i3−1−i300000000000000000000000000000000
χ2822222-2-2-2-222-2-222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2002222-2-2-2-200000000000000000000000000000000
χ2922222-2-2-2-222-2-22222−1−i3−1+i3−1−i3−1+i3222222-2-2-2-2-2-2-2-2−1−i3−1+i3−1−i3−1+i3−1−i3−1+i31+i31+i31−i31−i31+i31+i31−i31−i300−1−i3−1−i3−1+i3−1+i31+i31−i31+i31−i300000000000000000000000000000000
χ3022222-2-2-2-222-2-22222−1+i3−1−i3−1+i3−1−i3222222-2-2-2-2-2-2-2-2−1+i3−1−i3−1+i3−1−i3−1+i3−1−i31−i31−i31+i31+i31−i31−i31+i31+i300−1+i3−1+i3−1−i3−1−i31−i31+i31−i31+i300000000000000000000000000000000
χ3122-22-2002200-2022-2-2222200002-222-2-20000-2-222-2-200002222000000-2-200000000002i−2i0000002i−2i2i−2i000000000000
χ3222-22-2002200-2022-2-2222200002-222-2-20000-2-222-2-200002222000000-2-20000000000−2i2i000000−2i2i−2i2i000000000000
χ3322-22-2002200-2022-2-2−1−i3−1+i3−1−i3−1+i300002-222-2-200001+i31−i3−1−i3−1+i31+i31−i30000−1−i3−1−i3−1+i3−1+i30000001+i31−i300000000002i−2i0000002ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ166−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ1662ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ158−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ158000000000000
χ3422-22-2002200-2022-2-2−1−i3−1+i3−1−i3−1+i300002-222-2-200001+i31−i3−1−i3−1+i31+i31−i30000−1−i3−1−i3−1+i3−1+i30000001+i31−i30000000000−2i2i000000−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ1662ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ166−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ1582ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ158000000000000
χ3522-22-2002200-2022-2-2−1+i3−1−i3−1+i3−1−i300002-222-2-200001−i31+i3−1+i3−1−i31−i31+i30000−1+i3−1+i3−1−i3−1−i30000001−i31+i300000000002i−2i0000002ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ158−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ1582ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ166−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ166000000000000
χ3622-22-2002200-2022-2-2−1+i3−1−i3−1+i3−1−i300002-222-2-200001−i31+i3−1+i3−1−i31−i31+i30000−1+i3−1+i3−1−i3−1−i30000001−i31+i30000000000−2i2i000000−2ζ38−2ζ62−2ζ86−2ζ110−2ζ134−2ζ1582ζ38+2ζ62+2ζ86+2ζ110+2ζ134+2ζ158−2ζ22−2ζ46−2ζ94−2ζ118−2ζ142−2ζ1662ζ22+2ζ46+2ζ94+2ζ118+2ζ142+2ζ166000000000000
χ3722-22-200-2-2002022-2-2222200002-2-2-2220000-2-222-2-20000-2-2-2-2000000220000002-22200-2-200000000000000000000
χ3822-22-200-2-2002022-2-2222200002-2-2-2220000-2-222-2-20000-2-2-2-200000022000000-22-2-2002200000000000000000000
χ3922-22-200-2-2002022-2-2−1−i3−1+i3−1−i3−1+i300002-2-2-22200001+i31−i3−1−i3−1+i31+i31−i300001+i31+i31−i31−i3000000−1−i3−1+i30000002-2−1−i3−1+i3001+i31−i300000000000000000000
χ4022-22-200-2-2002022-2-2−1−i3−1+i3−1−i3−1+i300002-2-2-22200001+i31−i3−1−i3−1+i31+i31−i300001+i31+i31−i31−i3000000−1−i3−1+i3000000-221+i31−i300−1−i3−1+i300000000000000000000
χ4122-22-200-2-2002022-2-2−1+i3−1−i3−1+i3−1−i300002-2-2-22200001−i31+i3−1+i3−1−i31−i31+i300001−i31−i31+i31+i3000000−1+i3−1−i30000002-2−1+i3−1−i3001−i31+i300000000000000000000
χ4222-22-200-2-2002022-2-2−1+i3−1−i3−1+i3−1−i300002-2-2-22200001−i31+i3−1+i3−1−i31−i31+i300001−i31−i31+i31+i3000000−1+i3−1−i3000000-221−i31+i300−1+i3−1−i300000000000000000000
χ4322-2-222200000-222-2-222220000-22000022-2-2-2-2-2-2222222000000000000-2-2000000000000−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i20000
χ4422-2-222200000-222-2-222220000-22000022-2-2-2-2-2-2222222000000000000-2-2000000000000i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i20000
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χ8512-12000−6i26i2−6i26i26-600-222i7−2i70000−1+i7−1−i71−i71+i700i2−i2−1414i2−i2−141400000000000000000000000000000000000000000000000000000000
χ8612-12000−6i26i26i2−6i2-6600-22−2i72i700001+i71−i7−1−i7−1+i700−i2i2−1414i2−i214−1400000000000000000000000000000000000000000000000000000000
χ8712-12000−6i26i26i2−6i2-6600-222i7−2i700001−i71+i7−1+i7−1−i700−i2i214−14i2−i2−141400000000000000000000000000000000000000000000000000000000
χ8812-120006i2−6i2−6i26i2-6600-22−2i72i700001+i71−i7−1−i7−1+i700i2−i214−14−i2i2−141400000000000000000000000000000000000000000000000000000000
χ8912-120006i2−6i2−6i26i2-6600-222i7−2i700001−i71+i7−1+i7−1−i700i2−i2−1414−i2i214−1400000000000000000000000000000000000000000000000000000000
χ9012-120006i2−6i26i2−6i26-600-22−2i72i70000−1−i7−1+i71+i71−i700−i2i2−1414−i2i2−141400000000000000000000000000000000000000000000000000000000
χ9112-120006i2−6i26i2−6i26-600-222i7−2i70000−1+i7−1−i71−i71+i700−i2i214−14−i2i214−1400000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 168 (ζ168 = 1); i = ζ42.