Finite Group Databasebeta

← Group #285704

Character table — Group #285704

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444224444888888888888888844444444488888888888888884444888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-111111111-1-111-1-11111-1-1-1-111111111-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-111111111-1-111-1-11111-1-1-1-111111111-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-11
χ1111111111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-11111-1-1-11
χ1211111111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1111-1
χ1311111111-1-1-1-111111111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-11
χ1411111111-1-1-1-111111111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-1
χ1511111111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-111-1-1111-1
χ1611111111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1111111-1-111-1-1-11
χ172222222222222-2-2-2222-2-2-2-2-2220000000000000000-222-2-222-2-200000000000000000000000000
χ182222222222222-2-2-2222-2-2-2-2-2220000000000000000-2-2-222-2-22200000000000000000000000000
χ19222222222222-2222-2-2-2222-2-2-2-22222222200000000-200000000-2-200000000-2-200000000000000
χ20222222222222-2222-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-200000000-20000000022000000002200000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-222-2-2000000002i2i2i2i−2i−2i−2i−2i2000000000000000000002i2i−2i−2i0000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-222-2-200000000−2i−2i−2i−2i2i2i2i2i200000000000000000000−2i−2i2i2i0000000000
χ2322222222-2-2-2-22-2-2-2222-222-2-2-2-20000000000000000222-2-2-2-22200000000000000000000000000
χ2422222222-2-2-2-22-2-2-2222-222-2-2-2-200000000000000002-2-22222-2-200000000000000000000000000
χ2522222222-2-2-2-2-2222-2-2-22-2-2-2-2222222-2-2-2-2000000002000000002200000000-2-200000000000000
χ2622222222-2-2-2-2-2222-2-2-22-2-2-2-222-2-2-2-2222200000000200000000-2-2000000002200000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222000000002i2i2i2i−2i−2i−2i−2i-200000000000000000000−2i−2i2i2i0000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200000000−2i−2i−2i−2i2i2i2i2i-2000000000000000000002i2i−2i−2i0000000000
χ292222-2-2-2-222-2-202-2-200022-200002i2i−2i−2i2i2i−2i−2i0000000000000000000i2i2−i2−i2i2i2−i2−i200000000002−22−200
χ302222-2-2-2-222-2-202-2-200022-200002i2i−2i−2i2i2i−2i−2i0000000000000000000−i2−i2i2i2−i2−i2i2i20000000000−22−2200
χ312222-2-2-2-222-2-202-2-200022-20000−2i−2i2i2i−2i−2i2i2i0000000000000000000i2i2−i2−i2i2i2−i2−i20000000000−22−2200
χ322222-2-2-2-222-2-202-2-200022-20000−2i−2i2i2i−2i−2i2i2i0000000000000000000−i2−i2i2i2−i2−i2i2i200000000002−22−200
χ332222-2-2-2-2-2-22202-2-20002-2200002i2i−2i−2i−2i−2i2i2i0000000000000000000i2i2−i2−i2−i2−i2i2i200000000002−2−2200
χ342222-2-2-2-2-2-22202-2-20002-2200002i2i−2i−2i−2i−2i2i2i0000000000000000000−i2−i2i2i2i2i2−i2−i20000000000−222−200
χ352222-2-2-2-2-2-22202-2-20002-220000−2i−2i2i2i2i2i−2i−2i0000000000000000000i2i2−i2−i2−i2−i2i2i20000000000−222−200
χ362222-2-2-2-2-2-22202-2-20002-220000−2i−2i2i2i2i2i−2i−2i0000000000000000000−i2−i2i2i2i2i2−i2−i200000000002−2−2200
χ3722-2-22-22-22i−2i2i−2i2000-2-22000002i−2i2−22−2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i20002i−2i002-2i2−i2000000002−22−22−20000000000
χ3822-2-22-22-22i−2i2i−2i2000-2-22000002i−2i2−22−2i2−i2i2−i2−i2−i2i2i2−i2−i2i2i2000−2i2i00-22i2−i2000000002−2−22−220000000000
χ3922-2-22-22-22i−2i2i−2i2000-2-22000002i−2i−22−22−i2i2−i2i2i2i2−i2−i2i2i2−i2−i2000−2i2i00-22−i2i200000000−222−22−20000000000
χ4022-2-22-22-22i−2i2i−2i2000-2-22000002i−2i−22−22−i2i2−i2i2−i2−i2i2i2−i2−i2i2i20002i−2i002-2−i2i200000000−22−22−220000000000
χ4122-2-22-22-22i−2i2i−2i-200022-200000−2i2i2−22−2i2−i2i2−i222−2−2−2−22202-2002i−2i00−i2i200000000−22−i2i2i2−i20000000000
χ4222-2-22-22-22i−2i2i−2i-200022-200000−2i2i2−22−2i2−i2i2−i2−2−22222−2−20-2200−2i2i00−i2i200000000−22i2−i2−i2i20000000000
χ4322-2-22-22-22i−2i2i−2i-200022-200000−2i2i−22−22−i2i2−i2i222−2−2−2−2220-2200−2i2i00i2−i2000000002−2−i2i2i2−i20000000000
χ4422-2-22-22-22i−2i2i−2i-200022-200000−2i2i−22−22−i2i2−i2i2−2−22222−2−202-2002i−2i00i2−i2000000002−2i2−i2−i2i20000000000
χ4522-2-22-22-2−2i2i−2i2i2000-2-2200000−2i2i2−22−2−i2i2−i2i2i2i2−i2−i2i2i2−i2−i20002i−2i00-22−i2i2000000002−2−22−220000000000
χ4622-2-22-22-2−2i2i−2i2i2000-2-2200000−2i2i2−22−2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2000−2i2i002-2−i2i2000000002−22−22−20000000000
χ4722-2-22-22-2−2i2i−2i2i2000-2-2200000−2i2i−22−22i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2000−2i2i002-2i2−i200000000−22−22−220000000000
χ4822-2-22-22-2−2i2i−2i2i2000-2-2200000−2i2i−22−22i2−i2i2−i2−i2−i2i2i2−i2−i2i2i20002i−2i00-22i2−i200000000−222−22−20000000000
χ4922-2-22-22-2−2i2i−2i2i-200022-2000002i−2i2−22−2−i2i2−i2i222−2−2−2−22202-200−2i2i00i2−i200000000−22i2−i2−i2i20000000000
χ5022-2-22-22-2−2i2i−2i2i-200022-2000002i−2i2−22−2−i2i2−i2i2−2−22222−2−20-22002i−2i00i2−i200000000−22−i2i2i2−i20000000000
χ5122-2-22-22-2−2i2i−2i2i-200022-2000002i−2i−22−22i2−i2i2−i222−2−2−2−2220-22002i−2i00−i2i2000000002−2i2−i2−i2i20000000000
χ5222-2-22-22-2−2i2i−2i2i-200022-2000002i−2i−22−22i2−i2i2−i2−2−22222−2−202-200−2i2i00−i2i2000000002−2−i2i2i2−i20000000000
χ532-22-222-2-200002-22-22-2-22002-200000000002-22-22-22-20000000000000002i−2i2i−2i000000002i−2i000000
χ542-22-222-2-200002-22-22-2-22002-200000000002-22-22-22-2000000000000000−2i2i−2i2i00000000−2i2i000000
χ552-22-222-2-200002-22-22-2-22002-20000000000-22-22-22-220000000000000002i−2i2i−2i00000000−2i2i000000
χ562-22-222-2-200002-22-22-2-22002-20000000000-22-22-22-22000000000000000−2i2i−2i2i000000002i−2i000000
χ572-22-222-2-20000-22-22-222-2002-200000000002i−2i2i−2i−2i2i−2i2i000000000002-22-200000000002i−2i00000000
χ582-22-222-2-20000-22-22-222-2002-200000000002i−2i2i−2i−2i2i−2i2i00000000000-22-220000000000−2i2i00000000
χ592-22-222-2-20000-22-22-222-2002-20000000000−2i2i−2i2i2i−2i2i−2i000000000002-22-20000000000−2i2i00000000
χ602-22-222-2-20000-22-22-222-2002-20000000000−2i2i−2i2i2i−2i2i−2i00000000000-22-2200000000002i−2i00000000
χ614444-4-4-4-444-4-40-444000-4-440000000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4-4440-444000-44-40000000000000000000000000000000000000000000000000000000
χ6344-4-4-44-444i−4i−4i4i000000000000002i2−2i2−2i22i2−222222−220000000000000000000000000000000000000000000
χ6444-4-4-44-444i−4i−4i4i00000000000000−2i22i22i2−2i222−22−22220000000000000000000000000000000000000000000
χ6544-4-4-44-44−4i4i4i−4i000000000000002i2−2i2−2i22i222−22−22220000000000000000000000000000000000000000000
χ6644-4-4-44-44−4i4i4i−4i00000000000000−2i22i22i2−2i2−222222−220000000000000000000000000000000000000000000
χ674-44-444-4-4000044-444-4-4-400-4400000000000000000000000000000000000000000000000000000
χ684-44-444-4-40000-4-44-4-444400-4400000000000000000000000000000000000000000000000000000
χ694-44-4-4-4440000044-4000-40000000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ704-44-4-4-4440000044-4000-4000000000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ714-44-4-4-44400000-4-440004000000000000000000000000000000000000022−22−22220000000000000000
χ724-44-4-4-44400000-4-4400040000000000000000000000000000000000000−222222−220000000000000000
χ734-4-444-4-4400004000-44-40000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ744-4-444-4-4400004000-44-4000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ754-4-444-4-440000-40004-4400000000000000022−22−2222−222222−2200000000000000000000000000000000000
χ764-4-444-4-440000-40004-44000000000000000−222222−2222−22−222200000000000000000000000000000000000
χ778-8-88-888-8000000000000000000000000000000000000000000000000000000000000000000000

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