Finite Group Databasebeta

← Group #285652

Character table — Group #285652

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444224444888888888888888844444444488888888888888884444888844
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
χ911111111-1-1-1-111111111-1-111-1-11111-1-1-1-111111111-111-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-111111111-1-111-1-11111-1-1-1-111111111-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-11
χ1111111111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1111111-1-11111-1-1-11
χ1211111111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111111111-1-1-1-1111-1
χ1311111111-1-1-1-111111111-1-111-1-1-1-1-1-1111111111111-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-11
χ1411111111-1-1-1-111111111-1-111-1-1-1-1-1-1111111111111-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11-1
χ1511111111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-11111-1-111-1-1111-1
χ1611111111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-1111111-1-111-1-1-11
χ172222222222222-2-2-2222-2-2-2-2-2220000000000000000-22222-2-2-2-200000000000000000000000000
χ182222222222222-2-2-2222-2-2-2-2-2220000000000000000-2-2-2-2-2222200000000000000000000000000
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
χ292222-2-2-2-222-2-2022-2000-22-2000022-2-222-2-2000000000000000000022−2−222−2−200000000002−22−200
χ302222-2-2-2-222-2-2022-2000-22-2000022-2-222-2-20000000000000000000−2−222−2−2220000000000−22−2200
χ312222-2-2-2-222-2-2022-2000-22-20000-2-222-2-222000000000000000000022−2−222−2−20000000000−22−2200
χ322222-2-2-2-222-2-2022-2000-22-20000-2-222-2-2220000000000000000000−2−222−2−22200000000002−22−200
χ332222-2-2-2-2-2-222022-2000-2-22000022-2-2-2-222000000000000000000022−2−2−2−22200000000002−2−2200
χ342222-2-2-2-2-2-222022-2000-2-22000022-2-2-2-2220000000000000000000−2−22222−2−20000000000−222−200
χ352222-2-2-2-2-2-222022-2000-2-220000-2-22222-2-2000000000000000000022−2−2−2−2220000000000−222−200
χ362222-2-2-2-2-2-222022-2000-2-220000-2-22222-2-20000000000000000000−2−22222−2−200000000002−2−2200
χ3722-2-22-2-222i−2i2i−2i2000-2-22000002i−2i2−22−2i2−i2i2−i222−2−222−2−202-22i−2i0000i2−i2000000002−2i2−i2i2−i20000000000
χ3822-2-22-2-222i−2i2i−2i2000-2-22000002i−2i2−22−2i2−i2i2−i2−2−222−2−2220-22−2i2i0000i2−i2000000002−2−i2i2−i2i20000000000
χ3922-2-22-2-222i−2i2i−2i2000-2-22000002i−2i−22−22−i2i2−i2i222−2−222−2−20-22−2i2i0000−i2i200000000−22i2−i2i2−i20000000000
χ4022-2-22-2-222i−2i2i−2i2000-2-22000002i−2i−22−22−i2i2−i2i2−2−222−2−22202-22i−2i0000−i2i200000000−22−i2i2−i2i20000000000
χ4122-2-22-2-222i−2i2i−2i-200022-200000−2i2i2−22−2i2−i2i2−i2i2i2−i2−i2−i2−i2i2i2000002i−2i2-2−i2i200000000−22−222−20000000000
χ4222-2-22-2-222i−2i2i−2i-200022-200000−2i2i2−22−2i2−i2i2−i2−i2−i2i2i2i2i2−i2−i200000−2i2i-22−i2i200000000−222−2−220000000000
χ4322-2-22-2-222i−2i2i−2i-200022-200000−2i2i−22−22−i2i2−i2i2i2i2−i2−i2−i2−i2i2i200000−2i2i-22i2−i2000000002−2−222−20000000000
χ4422-2-22-2-222i−2i2i−2i-200022-200000−2i2i−22−22−i2i2−i2i2−i2−i2i2i2i2i2−i2−i2000002i−2i2-2i2−i2000000002−22−2−220000000000
χ4522-2-22-2-22−2i2i−2i2i2000-2-2200000−2i2i2−22−2−i2i2−i2i222−2−222−2−202-2−2i2i0000−i2i2000000002−2−i2i2−i2i20000000000
χ4622-2-22-2-22−2i2i−2i2i2000-2-2200000−2i2i2−22−2−i2i2−i2i2−2−222−2−2220-222i−2i0000−i2i2000000002−2i2−i2i2−i20000000000
χ4722-2-22-2-22−2i2i−2i2i2000-2-2200000−2i2i−22−22i2−i2i2−i222−2−222−2−20-222i−2i0000i2−i200000000−22−i2i2−i2i20000000000
χ4822-2-22-2-22−2i2i−2i2i2000-2-2200000−2i2i−22−22i2−i2i2−i2−2−222−2−22202-2−2i2i0000i2−i200000000−22i2−i2i2−i20000000000
χ4922-2-22-2-22−2i2i−2i2i-200022-2000002i−2i2−22−2−i2i2−i2i2i2i2−i2−i2−i2−i2i2i2000002i−2i-22i2−i200000000−222−2−220000000000
χ5022-2-22-2-22−2i2i−2i2i-200022-2000002i−2i2−22−2−i2i2−i2i2−i2−i2i2i2i2i2−i2−i200000−2i2i2-2i2−i200000000−22−222−20000000000
χ5122-2-22-2-22−2i2i−2i2i-200022-2000002i−2i−22−22i2−i2i2−i2i2i2−i2−i2−i2−i2i2i200000−2i2i2-2−i2i2000000002−22−2−220000000000
χ5222-2-22-2-22−2i2i−2i2i-200022-2000002i−2i−22−22i2−i2i2−i2−i2−i2i2i2i2i2−i2−i2000002i−2i-22−i2i2000000002−2−222−20000000000
χ532-2-222-22-2000022-2-22-2-22002-200000000002-22-22-22-20000000000000002i−2i2i−2i000000002i−2i000000
χ542-2-222-22-2000022-2-22-2-22002-200000000002-22-22-22-2000000000000000−2i2i−2i2i00000000−2i2i000000
χ552-2-222-22-2000022-2-22-2-22002-20000000000-22-22-22-220000000000000002i−2i2i−2i00000000−2i2i000000
χ562-2-222-22-2000022-2-22-2-22002-20000000000-22-22-22-22000000000000000−2i2i−2i2i000000002i−2i000000
χ572-2-222-22-20000-2-222-222-2002-200000000002i−2i2i−2i−2i2i−2i2i000000000002-22-200000000002i−2i00000000
χ582-2-222-22-20000-2-222-222-2002-200000000002i−2i2i−2i−2i2i−2i2i00000000000-22-220000000000−2i2i00000000
χ592-2-222-22-20000-2-222-222-2002-20000000000−2i2i−2i2i2i−2i2i−2i000000000002-22-20000000000−2i2i00000000
χ602-2-222-22-20000-2-222-222-2002-20000000000−2i2i−2i2i2i−2i2i−2i00000000000-22-2200000000002i−2i00000000
χ614444-4-4-4-444-4-40-4-440004-440000000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4-4440-4-4400044-40000000000000000000000000000000000000000000000000000000
χ6344-4-4-444-44i−4i−4i4i0000000000000022−22−22222i2−2i2−2i22i20000000000000000000000000000000000000000000
χ6444-4-4-444-44i−4i−4i4i00000000000000−222222−22−2i22i22i2−2i20000000000000000000000000000000000000000000
χ6544-4-4-444-4−4i4i4i−4i0000000000000022−22−2222−2i22i22i2−2i20000000000000000000000000000000000000000000
χ6644-4-4-444-4−4i4i4i−4i00000000000000−222222−222i2−2i2−2i22i20000000000000000000000000000000000000000000
χ674-44-444-4-400004000-44-400000000000000022−22−222222−22−222200000000000000000000000000000000000
χ684-44-444-4-400004000-44-4000000000000000−222222−22−222222−2200000000000000000000000000000000000
χ694-44-444-4-40000-40004-440000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000
χ704-44-444-4-40000-40004-44000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000
χ714-4-444-44-400004-4444-4-4-400-4400000000000000000000000000000000000000000000000000000
χ724-4-444-44-40000-44-4-4-444400-4400000000000000000000000000000000000000000000000000000
χ734-4-44-44-44000004-44000-400000000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ744-4-44-44-44000004-44000-40000000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ754-4-44-44-4400000-44-4000400000000000000000000000000000000022−22−222200000000000000000000
χ764-4-44-44-4400000-44-40004000000000000000000000000000000000−222222−2200000000000000000000
χ778-88-8-8-888000000000000000000000000000000000000000000000000000000000000000000000

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