Finite Group Databasebeta

← Group #148756

Character table — Group #148756

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order122222222222444444448888888844444444888888888888161616161616161616161616161616164444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111
χ91-1-1-111-1111-1-1111-1-1-11-111-1-111-1-1iiii−i−i−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-11-1ii−i−i1-111-1-1ii−i−i
χ101-1-1-111-1111-1-1111-1-1-11-111-1-111-1-1iiii−i−i−i−i11-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-11−i−iii-11-1-111−i−iii
χ111-1-1-111-1111-1-1111-1-1-11-111-1-111-1-1iiii−i−i−i−i11-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111-1−i−iii1-1-1-111ii−i−i
χ121-1-1-111-1111-1-1111-1-1-11-111-1-111-1-1iiii−i−i−i−i11-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111-11ii−i−i-1111-1-1−i−iii
χ131-1-1-111-1111-1-1111-1-1-11-111-1-111-1-1−i−i−i−iiiii11-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111-1ii−i−i1-1-1-111−i−iii
χ141-1-1-111-1111-1-1111-1-1-11-111-1-111-1-1−i−i−i−iiiii11-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111-11−i−iii-1111-1-1ii−i−i
χ151-1-1-111-1111-1-1111-1-1-11-111-1-111-1-1−i−i−i−iiiii11-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-11-1−i−iii1-111-1-1−i−iii
χ161-1-1-111-1111-1-1111-1-1-11-111-1-111-1-1−i−i−i−iiiii11-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1-11ii−i−i-11-1-111ii−i−i
χ1722222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ1922222222-2-2-2-222-22-2-2-220000000000000000000022-2-222-2-222−2−222−2−222−2−222−2−20000000000000000
χ2022222222-2-2-2-222-22-2-2-220000000000000000000022-2-222-2-2−2−222−2−222−2−222−2−2220000000000000000
χ2122222222-2-2-2-222-22-2-2-2200000000000000000000-2-222-2-22222−2−222−2−2−2−222−2−2220000000000000000
χ2222222222-2-2-2-222-22-2-2-2200000000000000000000-2-222-2-222−2−222−2−22222−2−222−2−20000000000000000
χ2322222222-2-2-2-2-2-22-2222-22222222200000000-2-2-2-2000000000000000000000000220000-2-200000000
χ2422222222-2-2-2-2-2-22-2222-22222222200000000-2-2-2-2000000000000000000000000-2-200002200000000
χ2522222222-2-2-2-2-2-22-2222-2-2-2-2-2-2-2-2-20000000022220000000000000000000000000000000000002i−2i2i−2i
χ2622222222-2-2-2-2-2-22-2222-2-2-2-2-2-2-2-2-2000000002222000000000000000000000000000000000000−2i2i−2i2i
χ27222-22-2-2-22-22-22-2-222-22-222-2-2-2-222000000002-22-2000000002-22-22-22-2000000000000000000000000
χ28222-22-2-2-22-22-22-2-222-22-222-2-2-2-222000000002-22-200000000-22-22-22-22000000000000000000000000
χ29222-22-2-2-22-22-22-2-222-22-2-2-22222-2-200000000-22-2200000000000000002-22-22-22-20000000000000000
χ30222-22-2-2-22-22-22-2-222-22-2-2-22222-2-200000000-22-220000000000000000-22-22-22-220000000000000000
χ31222-22-2-2-2-22-222-222-22-2-20000000022-2-222-2-20000000000002−2−222−2−222−2−222−2−220000000000000000
χ32222-22-2-2-2-22-222-222-22-2-20000000022-2-222-2-2000000000000−222−2−222−2−222−2−222−20000000000000000
χ33222-22-2-2-2-22-222-222-22-2-200000000-2-222-2-2220000000000002−2−222−2−22−222−2−222−20000000000000000
χ34222-22-2-2-2-22-222-222-22-2-200000000-2-222-2-222000000000000−222−2−222−22−2−222−2−220000000000000000
χ35222-22-2-2-2-22-22-22-2-22-22222-2-2-2-22200000000-22-22000000000000000000000000002i−2i2i−2i0000000000
χ36222-22-2-2-2-22-22-22-2-22-22222-2-2-2-22200000000-22-2200000000000000000000000000−2i2i−2i2i0000000000
χ37222-22-2-2-2-22-22-22-2-22-222-2-22222-2-2000000002-22-2000000000000000000000000000000002i−2i2i−2i0000
χ38222-22-2-2-2-22-22-22-2-22-222-2-22222-2-2000000002-22-200000000000000000000000000000000−2i2i−2i2i0000
χ392-2-222-22-22-2-222-2-2-2-22222222-2-2-2-2000000002-2-22000000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ402-2-222-22-22-2-222-2-2-2-22222222-2-2-2-2000000002-2-2200000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ412-2-222-22-22-2-222-2-2-2-2222-2-2-2-2222200000000-222-200000000000000002-22-2-22-220000000000000000
χ422-2-222-22-22-2-222-2-2-2-2222-2-2-2-2222200000000-222-20000000000000000-22-222-22-20000000000000000
χ432-2-222-22-2-222-22-22-22-2-22000000002i2i−2i−2i−2i−2i2i2i000000000000i2−i2−i2i2−i2i2i2−i22−2−22−222−20000000000000000
χ442-2-222-22-2-222-22-22-22-2-22000000002i2i−2i−2i−2i−2i2i2i000000000000−i2i2i2−i2i2−i2−i2i2−222−22−2−220000000000000000
χ452-2-222-22-2-222-22-22-22-2-2200000000−2i−2i2i2i2i2i−2i−2i000000000000i2−i2−i2i2−i2i2i2−i2−222−22−2−220000000000000000
χ462-2-222-22-2-222-22-22-22-2-2200000000−2i−2i2i2i2i2i−2i−2i000000000000−i2i2i2−i2i2−i2−i2i22−2−22−222−20000000000000000
χ472-2-222-22-2-222-2-22-22-222-22222-2-2-2-200000000-222-2000000000000000000000000002-2-220000000000
χ482-2-222-22-2-222-2-22-22-222-22222-2-2-2-200000000-222-200000000000000000000000000-222-20000000000
χ492-2-222-22-2-222-2-22-22-222-2-2-2-2-22222000000002-2-22000000000000000000000000000000002i−2i−2i2i0000
χ502-2-222-22-2-222-2-22-22-222-2-2-2-2-22222000000002-2-2200000000000000000000000000000000−2i2i2i−2i0000
χ512-2-2-222-2222-2-2222-2-2-22-2-2-222-2-2222i2i2i2i−2i−2i−2i−2i-2-222−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ522-2-2-222-2222-2-2222-2-2-22-2-2-222-2-222−2i−2i−2i−2i2i2i2i2i-2-2222i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ532-2-2-222-22-2-22222-2-222-2-2000000000000000000002i2i−2i−2i−2i−2i2i2ii2i2−i2−i2−i2−i2i2i222−2−2−2−2220000000000000000
χ542-2-2-222-22-2-22222-2-222-2-2000000000000000000002i2i−2i−2i−2i−2i2i2i−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000000000000000
χ552-2-2-222-22-2-22222-2-222-2-200000000000000000000−2i−2i2i2i2i2i−2i−2ii2i2−i2−i2−i2−i2i2i2−2−22222−2−20000000000000000
χ562-2-2-222-22-2-22222-2-222-2-200000000000000000000−2i−2i2i2i2i2i−2i−2i−i2−i2i2i2i2i2−i2−i222−2−2−2−2220000000000000000
χ572-2-2-222-22-2-222-2-222-2-22222-2-222-2-200000000-2-2220000000000000000000000002-20000-2200000000
χ582-2-2-222-22-2-222-2-222-2-22222-2-222-2-200000000-2-222000000000000000000000000-2200002-200000000
χ592-2-2-222-22-2-222-2-222-2-222-2-222-2-2220000000022-2-20000000000000000000000000000000000002-2-22
χ602-2-2-222-22-2-222-2-222-2-222-2-222-2-2220000000022-2-2000000000000000000000000000000000000-222-2
χ61444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000000000
χ62444-44-4-4-44-44-4-444-4-44-44000000000000000000000000000000000000000000000000000000000000
χ6344-44-44-4-400000000000022−2222−2222−2222−222-22-22-22-200000022−220022−2200000000000000000000000000000000
χ6444-44-44-4-400000000000022−2222−2222−2222−22-22-22-22-22000000−222200−222200000000000000000000000000000000
χ6544-44-44-4-4000000000000−2222−2222−2222−22222-22-22-22-2000000−222200−222200000000000000000000000000000000
χ6644-44-44-4-4000000000000−2222−2222−2222−2222-22-22-22-2200000022−220022−2200000000000000000000000000000000
χ6744-4-4-4-44400000000000022−22−2222−222222−222-2-222-2-22000022−220022−220000000000000000000000000000000000
χ6844-4-4-4-44400000000000022−22−2222−222222−22-222-2-222-20000−222200−22220000000000000000000000000000000000
χ6944-4-4-4-444000000000000−222222−2222−22−22222-2-222-2-220000−222200−22220000000000000000000000000000000000
χ7044-4-4-4-444000000000000−222222−2222−22−2222-222-2-222-2000022−220022−220000000000000000000000000000000000
χ714-444-4-4-4400000000000022−2222−22−2222−22222i−2i−2i2i−2i2i2i−2i00002i2−2i200−2i22i20000000000000000000000000000000000
χ724-444-4-4-4400000000000022−2222−22−2222−2222−2i2i2i−2i2i−2i−2i2i0000−2i22i2002i2−2i20000000000000000000000000000000000
χ734-444-4-4-44000000000000−2222−222222−2222−222i−2i−2i2i−2i2i2i−2i0000−2i22i2002i2−2i20000000000000000000000000000000000
χ744-444-4-4-44000000000000−2222−222222−2222−22−2i2i2i−2i2i−2i−2i2i00002i2−2i200−2i22i20000000000000000000000000000000000
χ754-44-4-444-400000000000022−22−222222−22−22222i−2i2i−2i−2i2i−2i2i0000002i2−2i200−2i22i200000000000000000000000000000000
χ764-44-4-444-400000000000022−22−222222−22−2222−2i2i−2i2i2i−2i2i−2i000000−2i22i2002i2−2i200000000000000000000000000000000
χ774-44-4-444-4000000000000−222222−22−222222−222i−2i2i−2i−2i2i−2i2i000000−2i22i2002i2−2i200000000000000000000000000000000
χ784-44-4-444-4000000000000−222222−22−222222−22−2i2i−2i2i2i−2i2i−2i0000002i2−2i200−2i22i200000000000000000000000000000000
χ794-4-444-44-44-4-44-44444-4-4-4000000000000000000000000000000000000000000000000000000000000
χ804-4-4-444-4444-4-4-4-4-4444-44000000000000000000000000000000000000000000000000000000000000

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