Finite Group Databasebeta

← Group #283981

Character table — Group #283981

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444448888888822222244448888888888888888444444888824
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-11111-1-1-11
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-111-1-1111-1
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1
χ81111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1111-1-111-1-1-11
χ911111111111111111-1-1-1-1111111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-1-1-1-1-111
χ1011111111111111111-1-1-1-1111111111-1-111-1-111-1-111-1-1-1-111-1-1-1-111111-1-11-1-11111-1-1
χ1111111111111111111-1-1-1-1111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1111111-1-1
χ1211111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-111-111-1-1-1-111
χ1311111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-11111111-1-1-1-1-111-11
χ1411111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111111-1-1-1-1111-1-1-111-1-11-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-11111-1-1-111111-1-11-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1111-1-111-11
χ17222222222-2-2222-2-2-22222-200000000-2-2002200-2-2-2-200002200000000000000000000
χ18222222222-2-2222-2-2-22222-200000000-2-200-2-20022220000-2-200000000000000000000
χ19222222222-2-2222-2-2-2-2-2-2-2-20000000022002200-2-2220000-2-200000000000000000000
χ20222222222-2-2222-2-2-2-2-2-2-2-2000000002200-2-20022-2-200002200000000000000000000
χ2122222222-222-2-2-222-20000-22222-2-2-2-200220022000000000000000000-200-200000000
χ2222222222-222-2-2-222-20000-22222-2-2-2-200-2-200-2-2000000000000000000200200000000
χ2322222222-222-2-2-222-20000-2-2-2-2-22222002200-2-2000000000000000000-200200000000
χ2422222222-222-2-2-222-20000-2-2-2-2-2222200-2-20022000000000000000000200-200000000
χ2522-2-222-2-2-20022-20002i2i−2i−2i0i2i2−i2−i2i2i2−i2−i2000000002i−2i2-222−2−20022−2−2i2i2−i2−i2000000000000
χ2622-2-222-2-2-20022-20002i2i−2i−2i0i2i2−i2−i2i2i2−i2−i200000000−2i2i-2222−2−200−2−222−i2−i2i2i2000000000000
χ2722-2-222-2-2-20022-20002i2i−2i−2i0−i2−i2i2i2−i2−i2i2i2000000002i−2i2-2−2−22200−2−222−i2−i2i2i2000000000000
χ2822-2-222-2-2-20022-20002i2i−2i−2i0−i2−i2i2i2−i2−i2i2i200000000−2i2i-22−2−2220022−2−2i2i2−i2−i2000000000000
χ2922-2-222-2-2-20022-2000−2i−2i2i2i0i2i2−i2−i2i2i2−i2−i2000000002i−2i-22−2−2220022−2−2−i2−i2i2i2000000000000
χ3022-2-222-2-2-20022-2000−2i−2i2i2i0i2i2−i2−i2i2i2−i2−i200000000−2i2i2-2−2−22200−2−222i2i2−i2−i2000000000000
χ3122-2-222-2-2-20022-2000−2i−2i2i2i0−i2−i2i2i2−i2−i2i2i2000000002i−2i-2222−2−200−2−222i2i2−i2−i2000000000000
χ3222-2-222-2-2-20022-2000−2i−2i2i2i0−i2−i2i2i2−i2−i2i2i200000000−2i2i2-222−2−20022−2−2−i2−i2i2i2000000000000
χ332-22-22-2-22222-22-2-2-2-2000022i−2i2i−2i2i−2i2i−2i0000000000000000000000000002i−2i02-2000000
χ342-22-22-2-22222-22-2-2-2-2000022i−2i2i−2i2i−2i2i−2i000000000000000000000000000−2i2i0-22000000
χ352-22-22-2-22222-22-2-2-2-200002−2i2i−2i2i−2i2i−2i2i0000000000000000000000000002i−2i0-22000000
χ362-22-22-2-22222-22-2-2-2-200002−2i2i−2i2i−2i2i−2i2i000000000000000000000000000−2i2i02-2000000
χ372-22-22-2-22-2222-22-2-222-22-2-22i−2i2i−2i−2i2i−2i2i2-200000000002i−2i2i−2i0000000000000000000000
χ382-22-22-2-22-2222-22-2-222-22-2-2−2i2i−2i2i2i−2i2i−2i2-20000000000−2i2i−2i2i0000000000000000000000
χ392-22-22-2-22-2222-22-2-22-22-22-22i−2i2i−2i−2i2i−2i2i-220000000000−2i2i−2i2i0000000000000000000000
χ402-22-22-2-22-2222-22-2-22-22-22-2−2i2i−2i2i2i−2i2i−2i-2200000000002i−2i2i−2i0000000000000000000000
χ412-22-22-2-22-2-2-22-2222-22-22-2200000000-2200000000000000002-22-22-22-2000000000000
χ422-22-22-2-22-2-2-22-2222-22-22-2200000000-220000000000000000-22-22-22-22000000000000
χ432-22-22-2-22-2-2-22-2222-2-22-222000000002-200000000000000002-22-2-22-22000000000000
χ442-22-22-2-22-2-2-22-2222-2-22-222000000002-20000000000000000-22-222-22-2000000000000
χ452-2-222-22-22002-2-20002i−2i−2i2i02−2−22−222−200002-2000000−i2i2i2−i22i−2i2−2−22i2−i2−i2i2000000000000
χ462-2-222-22-22002-2-20002i−2i−2i2i02−2−22−222−20000-22000000−i2i2i2−i2−2i2i−222−2−i2i2i2−i2000000000000
χ472-2-222-22-22002-2-20002i−2i−2i2i0−222−22−2−2200002-2000000i2−i2−i2i22i−2i−222−2−i2i2i2−i2000000000000
χ482-2-222-22-22002-2-20002i−2i−2i2i0−222−22−2−220000-22000000i2−i2−i2i2−2i2i2−2−22i2−i2−i2i2000000000000
χ492-2-222-22-22002-2-2000−2i2i2i−2i02−2−22−222−200002-2000000i2−i2−i2i2−2i2i2−2−22−i2i2i2−i2000000000000
χ502-2-222-22-22002-2-2000−2i2i2i−2i02−2−22−222−20000-22000000i2−i2−i2i22i−2i−222−2i2−i2−i2i2000000000000
χ512-2-222-22-22002-2-2000−2i2i2i−2i0−222−22−2−2200002-2000000−i2i2i2−i2−2i2i−222−2i2−i2−i2i2000000000000
χ522-2-222-22-22002-2-2000−2i2i2i−2i0−222−22−2−220000-22000000−i2i2i2−i22i−2i2−2−22−i2i2i2−i2000000000000
χ5344444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000000000
χ5444-4-444-4-4400-4-44000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000000000000000
χ5544-4-444-4-4400-4-4400000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000000000000000
χ5644-4-4-4-44404-40004-4000000000000000000000000000000000000000000000022−220000
χ5744-4-4-4-44404-40004-40000000000000000000000000000000000000000000000−22220000
χ5844-4-4-4-4440-44000-4400000000000000004-40000000000000000000000000000000000
χ5944-4-4-4-4440-44000-440000000000000000-440000000000000000000000000000000000
χ604-44-44-4-444-4-4-44-44440000-40000000000000000000000000000000000000000000000
χ614-4-444-44-4-400-4440000000022−22−222222−22−222200000000000000000000000000000000000000
χ624-4-444-44-4-400-44400000000−222222−22−222222−2200000000000000000000000000000000000000
χ634-4-44-44-4404-4000-4400000000000000000000000000000000000000000000000022−2200
χ644-4-44-44-4404-4000-44000000000000000000000000000000000000000000000000−222200
χ654-4-44-44-440-440004-4000000000000000000004-4000000000000000000000000000000
χ664-4-44-44-440-440004-400000000000000000000-44000000000000000000000000000000
χ678888-8-8-8-8000000000000000000000000000000000000000000000000000000000000
χ688-88-8-888-8000000000000000000000000000000000000000000000000000000000000

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