Finite Group Databasebeta

← Group #281133

Character table — Group #281133

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888822224444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-1-11
χ61111111111111111111111-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1111-1
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111111-111-1-1-1-1111-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1-11111-1-1-11
χ911111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111
χ1011111111111111111-1-1-1-111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ1111111111111111111-1-1-1-1111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-111-1-111-11
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1111-1-111-1-11-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-11-1-1-11111-1-11-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1111-1-1-1-111-11
χ17222222222-2-22-2-222-20000-22222-2-2-2-200220022000000000000000000-2-20000000000
χ18222222222-2-22-2-222-20000-22222-2-2-2-200-2-200-2-2000000000000000000220000000000
χ19222222222-2-22-2-222-20000-2-2-2-2-22222002200-2-2000000000000000000-220000000000
χ20222222222-2-22-2-222-20000-2-2-2-2-2222200-2-200220000000000000000002-20000000000
χ2122222222-222-222-2-2-22222-2000000002200-2-200-2-222-2-2000000000000000000000000
χ2222222222-222-222-2-2-22222-200000000-2-2002200-2-2-2-222000000000000000000000000
χ2322222222-222-222-2-2-2-2-2-2-2-2000000002200-2-20022-2-222000000000000000000000000
χ2422222222-222-222-2-2-2-2-2-2-2-200000000-2-20022002222-2-2000000000000000000000000
χ25222-2-2-2-2202-202-20002i2i−2i−2i0i2i2−i2−i2i2i2−i2−i22-2000000002i−2i0022−2−2i2i2−i2−i222−2−2000000000000
χ26222-2-2-2-2202-202-20002i2i−2i−2i0i2i2−i2−i2i2i2−i2−i2-2200000000−2i2i0022−2−2−i2−i2i2i2−2−222000000000000
χ27222-2-2-2-2202-202-20002i2i−2i−2i0−i2−i2i2i2−i2−i2i2i22-2000000002i−2i00−2−222−i2−i2i2i2−2−222000000000000
χ28222-2-2-2-2202-202-20002i2i−2i−2i0−i2−i2i2i2−i2−i2i2i2-2200000000−2i2i00−2−222i2i2−i2−i222−2−2000000000000
χ29222-2-2-2-2202-202-2000−2i−2i2i2i0i2i2−i2−i2i2i2−i2−i22-200000000−2i2i00−2−222i2i2−i2−i2−2−222000000000000
χ30222-2-2-2-2202-202-2000−2i−2i2i2i0i2i2−i2−i2i2i2−i2−i2-22000000002i−2i00−2−222−i2−i2i2i222−2−2000000000000
χ31222-2-2-2-2202-202-2000−2i−2i2i2i0−i2−i2i2i2−i2−i2i2i22-200000000−2i2i0022−2−2−i2−i2i2i222−2−2000000000000
χ32222-2-2-2-2202-202-2000−2i−2i2i2i0−i2−i2i2i2−i2−i2i2i2-22000000002i−2i0022−2−2i2i2−i2−i2−2−222000000000000
χ332-222-22-2-22-2-2-2222-2-22i−2i2i−2i200000000000000002i−2i000000002i−2i2i−2i2-22-2000000000000
χ342-222-22-2-22-2-2-2222-2-22i−2i2i−2i200000000000000002i−2i00000000−2i2i−2i2i-22-22000000000000
χ352-222-22-2-22-2-2-2222-2-2−2i2i−2i2i20000000000000000−2i2i000000002i−2i2i−2i-22-22000000000000
χ362-222-22-2-22-2-2-2222-2-2−2i2i−2i2i20000000000000000−2i2i00000000−2i2i−2i2i2-22-2000000000000
χ372-222-22-2-2-2222-2-2-22-2000022-22-22-22-200000000000000000000000000002i−2i2i−2i000000
χ382-222-22-2-2-2222-2-2-22-2000022-22-22-22-20000000000000000000000000000−2i2i−2i2i000000
χ392-222-22-2-2-2222-2-2-22-200002-22-22-22-2200000000000000000000000000002i−2i−2i2i000000
χ402-222-22-2-2-2222-2-2-22-200002-22-22-22-220000000000000000000000000000−2i2i2i−2i000000
χ412-222-22-2-2-2-2-2222-2222i−2i2i−2i-22-22-2-22-2200000000−2i2i00002i−2i2i−2i00000000000000000000
χ422-222-22-2-2-2-2-2222-2222i−2i2i−2i-2-22-222-22-200000000−2i2i0000−2i2i−2i2i00000000000000000000
χ432-222-22-2-2-2-2-2222-222−2i2i−2i2i-22-22-2-22-22000000002i−2i0000−2i2i−2i2i00000000000000000000
χ442-222-22-2-2-2-2-2222-222−2i2i−2i2i-2-22-222-22-2000000002i−2i00002i−2i2i−2i00000000000000000000
χ452-22-22-22-20-2202-20002-2-220i2−i2−i2i2−i2i2i2−i200002i−2i0000002i−2i−i2i2i2−i22−2−222−2−22000000000000
χ462-22-22-22-20-2202-20002-2-220i2−i2−i2i2−i2i2i2−i20000−2i2i000000−2i2i−i2i2i2−i2−222−2−222−2000000000000
χ472-22-22-22-20-2202-20002-2-220−i2i2i2−i2i2−i2−i2i200002i−2i0000002i−2ii2−i2−i2i2−222−2−222−2000000000000
χ482-22-22-22-20-2202-20002-2-220−i2i2i2−i2i2−i2−i2i20000−2i2i000000−2i2ii2−i2−i2i22−2−222−2−22000000000000
χ492-22-22-22-20-2202-2000-222-20i2−i2−i2i2−i2i2i2−i200002i−2i000000−2i2ii2−i2−i2i22−2−22−222−2000000000000
χ502-22-22-22-20-2202-2000-222-20i2−i2−i2i2−i2i2i2−i20000−2i2i0000002i−2ii2−i2−i2i2−222−22−2−22000000000000
χ512-22-22-22-20-2202-2000-222-20−i2i2i2−i2i2−i2−i2i200002i−2i000000−2i2i−i2i2i2−i2−222−22−2−22000000000000
χ522-22-22-22-20-2202-2000-222-20−i2i2i2−i2i2−i2−i2i20000−2i2i0000002i−2i−i2i2i2−i22−2−22−222−2000000000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ54444-4-4-4-440-440-44000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ55444-4-4-4-440-440-4400000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ5644-4-444-4-4400400-4-4000000000000000000004-4000000000000000000000000000000
χ5744-4-444-4-4400400-4-400000000000000000000-44000000000000000000000000000000
χ5844-4-444-4-4-400-400440000000000000000000000000000000000000000000000002i2−2i200
χ5944-4-444-4-4-400-40044000000000000000000000000000000000000000000000000−2i22i200
χ604-444-44-4-4444-4-4-44-440000-40000000000000000000000000000000000000000000000
χ614-44-44-44-404-40-44000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ624-44-44-44-404-40-4400000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ634-4-4-4-4444400-400-44000000000000000000000000000000000000000000000022−220000
χ644-4-4-4-4444400-400-440000000000000000000000000000000000000000000000−22220000
χ654-4-4-4-4444-4004004-400000000000000004-40000000000000000000000000000000000
χ664-4-4-4-4444-4004004-40000000000000000-440000000000000000000000000000000000
χ6788-88-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-8-888-8-88000000000000000000000000000000000000000000000000000000000000

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