Finite Group Databasebeta

← Group #482155

Character table — Group #482155

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222444444444888888888888881616161616161111222244444444488888888888888161616161616
order12222244224444444444444888888884444442222224422444444444444488888888444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111-1-1-1-111111111-1-1-1-1-1-11111111111111111111-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111-1-1-1-1111-1-11-11111iiii−i−i−i−i-1-1ii−i−i11111111-1-1-1-1111-1-11-11111iiii−i−i−i−i-1-1ii−i−i
χ611111111-1-1-1-1111-1-11-11111−i−i−i−iiiii-1-1−i−iii11111111-1-1-1-1111-1-11-11111−i−i−i−iiiii-1-1−i−iii
χ711111111-1-1-1-1111-1-11-1-1-1-1-1iiii−i−i−i−i11−i−iii11111111-1-1-1-1111-1-11-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ811111111-1-1-1-1111-1-11-1-1-1-1-1−i−i−i−iiiii11ii−i−i11111111-1-1-1-1111-1-11-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ9111111-1-111-1-1-1-1-1111-111-1-111-1-111-1-11-11-11-1111111-1-111-1-1-1-1-1111-111-1-111-1-111-1-11-11-11-1
χ10111111-1-111-1-1-1-1-1111-111-1-1-1-111-1-1111-1-11-11111111-1-111-1-1-1-1-1111-111-1-1-1-111-1-1111-1-11-11
χ11111111-1-111-1-1-1-1-1111-1-1-11111-1-111-1-1-11-11-11111111-1-111-1-1-1-1-1111-1-1-11111-1-111-1-1-11-11-11
χ12111111-1-111-1-1-1-1-1111-1-1-111-1-111-1-111-111-11-1111111-1-111-1-1-1-1-1111-1-1-111-1-111-1-111-111-11-1
χ13111111-1-1-1-111-1-1-1-1-11111-1-1ii−i−i−i−iii-11i−i−ii111111-1-1-1-111-1-1-1-1-11111-1-1ii−i−i−i−iii-11i−i−ii
χ14111111-1-1-1-111-1-1-1-1-11111-1-1−i−iiiii−i−i-11−iii−i111111-1-1-1-111-1-1-1-1-11111-1-1−i−iiiii−i−i-11−iii−i
χ15111111-1-1-1-111-1-1-1-1-111-1-111ii−i−i−i−iii1-1−iii−i111111-1-1-1-111-1-1-1-1-111-1-111ii−i−i−i−iii1-1−iii−i
χ16111111-1-1-1-111-1-1-1-1-111-1-111−i−iiiii−i−i1-1i−i−ii111111-1-1-1-111-1-1-1-1-111-1-111−i−iiiii−i−i1-1i−i−ii
χ172222222222-2-22-2-2-2-2-220000000000000000002222222222-2-22-2-2-2-2-22000000000000000000
χ1822222222-2-2222-2-222-2-200000000000000000022222222-2-2222-2-222-2-2000000000000000000
χ19222222-2-22222-222-2-2-2-2000000000000000000222222-2-22222-222-2-2-2-2000000000000000000
χ20222222-2-2-2-2-2-2-22222-22000000000000000000222222-2-2-2-2-2-2-22222-22000000000000000000
χ212-22-22-2002-22i−2i02i−2i00000000i2−i22−2i2−i22−20000002-22-22-2002-22i−2i02i−2i00000000i2−i22−2i2−i22−2000000
χ222-22-22-2002-22i−2i02i−2i00000000−i2i2−22−i2i2−220000002-22-22-2002-22i−2i02i−2i00000000−i2i2−22−i2i2−22000000
χ232-22-22-2002-2−2i2i0−2i2i00000000i2−i2−22i2−i2−220000002-22-22-2002-2−2i2i0−2i2i00000000i2−i2−22i2−i2−22000000
χ242-22-22-2002-2−2i2i0−2i2i00000000−i2i22−2−i2i22−20000002-22-22-2002-2−2i2i0−2i2i00000000−i2i22−2−i2i22−2000000
χ252-22-22-200-222i−2i0−2i2i000000002−2i2−i2−22−i2i20000002-22-22-200-222i−2i0−2i2i000000002−2i2−i2−22−i2i2000000
χ262-22-22-200-222i−2i0−2i2i00000000−22−i2i22−2i2−i20000002-22-22-200-222i−2i0−2i2i00000000−22−i2i22−2i2−i2000000
χ272-22-22-200-22−2i2i02i−2i000000002−2−i2i2−22i2−i20000002-22-22-200-22−2i2i02i−2i000000002−2−i2i2−22i2−i2000000
χ282-22-22-200-22−2i2i02i−2i00000000−22i2−i22−2−i2i20000002-22-22-200-22−2i2i02i−2i00000000−22i2−i22−2−i2i2000000
χ294444-4-4440000-40000000000000000000000004444-4-4440000-4000000000000000000000000
χ304444-4-4-4-4000040000000000000000000000004444-4-4-4-400004000000000000000000000000
χ314-44-4-440000000004i−4i000000000000000000004-44-4-440000000004i−4i00000000000000000000
χ324-44-4-44000000000−4i4i000000000000000000004-44-4-44000000000−4i4i00000000000000000000
χ334-4-44004i−4i000000000002i−2i2-2000000000000004-4-44004i−4i000000000002i−2i2-200000000000000
χ344-4-44004i−4i00000000000−2i2i-22000000000000004-4-44004i−4i00000000000−2i2i-2200000000000000
χ354-4-4400−4i4i000000000002i−2i-22000000000000004-4-4400−4i4i000000000002i−2i-2200000000000000
χ364-4-4400−4i4i00000000000−2i2i2-2000000000000004-4-4400−4i4i00000000000−2i2i2-200000000000000
χ3788-8-800000000000000000000000000000000088-8-8000000000000000000000000000000000
χ381111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3911111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111
χ401111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1
χ4211111111-1-1-1-1111-1-11-11111iiii−i−i−i−i-1-1ii−i−i-1-1-1-1-1-1-1-11111-1-1-111-11-1-1-1-1−i−i−i−iiiii11−i−iii
χ4311111111-1-1-1-1111-1-11-11111−i−i−i−iiiii-1-1−i−iii-1-1-1-1-1-1-1-11111-1-1-111-11-1-1-1-1iiii−i−i−i−i11ii−i−i
χ4411111111-1-1-1-1111-1-11-1-1-1-1-1iiii−i−i−i−i11−i−iii-1-1-1-1-1-1-1-11111-1-1-111-111111−i−i−i−iiiii-1-1ii−i−i
χ4511111111-1-1-1-1111-1-11-1-1-1-1-1−i−i−i−iiiii11ii−i−i-1-1-1-1-1-1-1-11111-1-1-111-111111iiii−i−i−i−i-1-1−i−iii
χ46111111-1-111-1-1-1-1-1111-111-1-111-1-111-1-11-11-11-1-1-1-1-1-1-111-1-111111-1-1-11-1-111-1-111-1-111-11-11-11
χ47111111-1-111-1-1-1-1-1111-111-1-1-1-111-1-1111-1-11-11-1-1-1-1-1-111-1-111111-1-1-11-1-11111-1-111-1-1-111-11-1
χ48111111-1-111-1-1-1-1-1111-1-1-11111-1-111-1-1-11-11-11-1-1-1-1-1-111-1-111111-1-1-1111-1-1-1-111-1-1111-11-11-1
χ49111111-1-111-1-1-1-1-1111-1-1-111-1-111-1-111-111-11-1-1-1-1-1-1-111-1-111111-1-1-1111-1-111-1-111-1-11-1-11-11
χ50111111-1-1-1-111-1-1-1-1-11111-1-1ii−i−i−i−iii-11i−i−ii-1-1-1-1-1-11111-1-111111-1-1-1-111−i−iiiii−i−i1-1−iii−i
χ51111111-1-1-1-111-1-1-1-1-11111-1-1−i−iiiii−i−i-11−iii−i-1-1-1-1-1-11111-1-111111-1-1-1-111ii−i−i−i−iii1-1i−i−ii
χ52111111-1-1-1-111-1-1-1-1-111-1-111ii−i−i−i−iii1-1−iii−i-1-1-1-1-1-11111-1-111111-1-111-1-1−i−iiiii−i−i-11i−i−ii
χ53111111-1-1-1-111-1-1-1-1-111-1-111−i−iiiii−i−i1-1i−i−ii-1-1-1-1-1-11111-1-111111-1-111-1-1ii−i−i−i−iii-11−iii−i
χ542222222222-2-22-2-2-2-2-22000000000000000000-2-2-2-2-2-2-2-2-2-222-222222-2000000000000000000
χ5522222222-2-2222-2-222-2-2000000000000000000-2-2-2-2-2-2-2-222-2-2-222-2-222000000000000000000
χ56222222-2-22222-222-2-2-2-2000000000000000000-2-2-2-2-2-222-2-2-2-22-2-22222000000000000000000
χ57222222-2-2-2-2-2-2-22222-22000000000000000000-2-2-2-2-2-22222222-2-2-2-22-2000000000000000000
χ582-22-22-2002-22i−2i02i−2i00000000i2−i22−2i2−i22−2000000-22-22-2200-22−2i2i0−2i2i00000000−i2i2−22−i2i2−22000000
χ592-22-22-2002-22i−2i02i−2i00000000−i2i2−22−i2i2−22000000-22-22-2200-22−2i2i0−2i2i00000000i2−i22−2i2−i22−2000000
χ602-22-22-2002-2−2i2i0−2i2i00000000i2−i2−22i2−i2−22000000-22-22-2200-222i−2i02i−2i00000000−i2i22−2−i2i22−2000000
χ612-22-22-2002-2−2i2i0−2i2i00000000−i2i22−2−i2i22−2000000-22-22-2200-222i−2i02i−2i00000000i2−i2−22i2−i2−22000000
χ622-22-22-200-222i−2i0−2i2i000000002−2i2−i2−22−i2i2000000-22-22-22002-2−2i2i02i−2i00000000−22−i2i22−2i2−i2000000
χ632-22-22-200-222i−2i0−2i2i00000000−22−i2i22−2i2−i2000000-22-22-22002-2−2i2i02i−2i000000002−2i2−i2−22−i2i2000000
χ642-22-22-200-22−2i2i02i−2i000000002−2−i2i2−22i2−i2000000-22-22-22002-22i−2i0−2i2i00000000−22i2−i22−2−i2i2000000
χ652-22-22-200-22−2i2i02i−2i00000000−22i2−i22−2−i2i2000000-22-22-22002-22i−2i0−2i2i000000002−2−i2i2−22i2−i2000000
χ664444-4-4440000-4000000000000000000000000-4-4-4-444-4-400004000000000000000000000000
χ674444-4-4-4-400004000000000000000000000000-4-4-4-444440000-4000000000000000000000000
χ684-44-4-440000000004i−4i00000000000000000000-44-444-4000000000−4i4i00000000000000000000
χ694-44-4-44000000000−4i4i00000000000000000000-44-444-40000000004i−4i00000000000000000000
χ704-4-44004i−4i000000000002i−2i2-200000000000000-444-400−4i4i00000000000−2i2i-2200000000000000
χ714-4-44004i−4i00000000000−2i2i-2200000000000000-444-400−4i4i000000000002i−2i2-200000000000000
χ724-4-4400−4i4i000000000002i−2i-2200000000000000-444-4004i−4i00000000000−2i2i2-200000000000000
χ734-4-4400−4i4i00000000000−2i2i2-200000000000000-444-4004i−4i000000000002i−2i-2200000000000000
χ7488-8-8000000000000000000000000000000000-8-888000000000000000000000000000000000

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