Finite Group Databasebeta

← Group #286721

Character table — Group #286721

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444888888888888888844444444488888888888888884444888824
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111111111-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1111111-1-1-1-1111111-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
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
χ91111111111-1-1-1-1111111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-111-1-1-1-111-11
χ101111111111-1-1-1-1111111-1-1-1-111111111111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-11-1
χ111111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-11111-1-11111-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11-1
χ121111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-11111-1-11111-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ131111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-11111111111-1-1-1-1-1-111-1-1111-1
χ141111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-11
χ151111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-11
χ161111111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1111-1
χ17222222222-2222222-2-22-222-2-2-2-20000000022222222000000-200-2-200000000-2-200000000000000
χ18222222222-2222222-2-22-222-2-2-2-200000000-2-2-2-2-2-2-2-2000000-20022000000002200000000000000
χ19222222222-2-2-2-2-222-2-22-2-2-222-2-2000000002222-2-2-2-20000002002200000000-2-200000000000000
χ20222222222-2-2-2-2-222-2-22-2-2-222-2-200000000-2-2-2-22222000000200-2-2000000002200000000000000
χ2122222222-222222-2-222-22-2-222-2-200000000000000002222-2-2-2-2-200000000000000000000000000
χ2222222222-222222-2-222-22-2-222-2-20000000000000000-2-2-2-222-22200000000000000000000000000
χ2322222222-22-2-2-2-2-2-222-2222-2-2-2-2000000000000000022-2-2222-2-200000000000000000000000000
χ2422222222-22-2-2-2-2-2-222-2222-2-2-2-20000000000000000-2-222-2-222200000000000000000000000000
χ2522222222-2-22222-2-2-2-2-2-2-2-2-2-2222i2i2i2i−2i−2i−2i−2i000000000000002000000002i2i−2i−2i0000000000000000
χ2622222222-2-22222-2-2-2-2-2-2-2-2-2-222−2i−2i−2i−2i2i2i2i2i00000000000000200000000−2i−2i2i2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222222i2i2i2i−2i−2i−2i−2i00000000000000-200000000−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222−2i−2i−2i−2i2i2i2i2i00000000000000-2000000002i2i−2i−2i0000000000000000
χ29222-2-2-2-222-200002-22-2-2200002-222-2-222-2-200000000000000000002i2i−2i−2i00000000002i−2i00000000
χ30222-2-2-2-222-200002-22-2-2200002-222-2-222-2-20000000000000000000−2i−2i2i2i0000000000−2i2i00000000
χ31222-2-2-2-222-200002-22-2-2200002-2-2-222-2-22200000000000000000002i2i−2i−2i0000000000−2i2i00000000
χ32222-2-2-2-222-200002-22-2-2200002-2-2-222-2-2220000000000000000000−2i−2i2i2i00000000002i−2i00000000
χ33222-2-2-2-22-220000-22-222-200002-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000002i2i−2i−2i002-2000000
χ34222-2-2-2-22-220000-22-222-200002-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000−2i−2i2i2i00-22000000
χ35222-2-2-2-22-220000-22-222-200002-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000002i2i−2i−2i00-22000000
χ36222-2-2-2-22-220000-22-222-200002-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000−2i−2i2i2i002-2000000
χ3722-22-2-22-2022i2i−2i−2i00-2-202002i−2i00i2−i2i2−i2i2−i2i2−i2i2i2−i2−i222−2−200002i−2i02-22−200002−22−2i2−i200000000000000
χ3822-22-2-22-2022i2i−2i−2i00-2-202002i−2i00i2−i2i2−i2i2−i2i2−i2−i2−i2i2i2−2−2220000−2i2i0-22−2200002−22−2−i2i200000000000000
χ3922-22-2-22-2022i2i−2i−2i00-2-202002i−2i00−i2i2−i2i2−i2i2−i2i2i2i2−i2−i222−2−20000−2i2i0-222−20000−22−22i2−i200000000000000
χ4022-22-2-22-2022i2i−2i−2i00-2-202002i−2i00−i2i2−i2i2−i2i2−i2i2−i2−i2i2i2−2−22200002i−2i02-2−220000−22−22−i2i200000000000000
χ4122-22-2-22-202−2i−2i2i2i00-2-20200−2i2i00i2−i2i2−i2i2−i2i2−i2i2i2−i2−i2−2−2220000−2i2i02-2−220000−22−22i2−i200000000000000
χ4222-22-2-22-202−2i−2i2i2i00-2-20200−2i2i00i2−i2i2−i2i2−i2i2−i2−i2−i2i2i222−2−200002i−2i0-222−20000−22−22−i2i200000000000000
χ4322-22-2-22-202−2i−2i2i2i00-2-20200−2i2i00−i2i2−i2i2−i2i2−i2i2i2i2−i2−i2−2−22200002i−2i0-22−2200002−22−2i2−i200000000000000
χ4422-22-2-22-202−2i−2i2i2i00-2-20200−2i2i00−i2i2−i2i2−i2i2−i2i2−i2−i2i2i222−2−20000−2i2i02-22−200002−22−2−i2i200000000000000
χ4522-22-2-22-20-22i2i−2i−2i00220-200−2i2i002−22−2−22−22i2i2−i2−i222−2−22i−2i2-200000−220000−i2i2i2−i2−i2i200000000000000
χ4622-22-2-22-20-22i2i−2i−2i00220-200−2i2i002−22−2−22−22−i2−i2i2i2−2−222−2i2i-22000002−20000−i2i2i2−i2i2−i200000000000000
χ4722-22-2-22-20-22i2i−2i−2i00220-200−2i2i00−22−222−22−2i2i2−i2−i222−2−2−2i2i-2200000−220000i2−i2−i2i2−i2i200000000000000
χ4822-22-2-22-20-22i2i−2i−2i00220-200−2i2i00−22−222−22−2−i2−i2i2i2−2−2222i−2i2-2000002−20000i2−i2−i2i2i2−i200000000000000
χ4922-22-2-22-20-2−2i−2i2i2i00220-2002i−2i002−22−2−22−22i2i2−i2−i2−2−2222i−2i-22000002−20000i2−i2−i2i2−i2i200000000000000
χ5022-22-2-22-20-2−2i−2i2i2i00220-2002i−2i002−22−2−22−22−i2−i2i2i222−2−2−2i2i2-200000−220000i2−i2−i2i2i2−i200000000000000
χ5122-22-2-22-20-2−2i−2i2i2i00220-2002i−2i00−22−222−22−2i2i2−i2−i2−2−222−2i2i2-2000002−20000−i2i2i2−i2−i2i200000000000000
χ5222-22-2-22-20-2−2i−2i2i2i00220-2002i−2i00−22−222−22−2−i2−i2i2i222−2−22i−2i-2200000−220000−i2i2i2−i2i2−i200000000000000
χ532-22-22-22-2202i−2i2i−2i-2-200202i−2i0000000000002i−2i2i−2i2-22-200000000000i2−i2i2−i20000002−22−20000i2−i22−200
χ542-22-22-22-2202i−2i2i−2i-2-200202i−2i0000000000002i−2i2i−2i2-22-200000000000−i2i2−i2i2000000−22−220000−i2i2−2200
χ552-22-22-22-2202i−2i2i−2i-2-200202i−2i000000000000−2i2i−2i2i-22-2200000000000i2−i2i2−i20000002−22−20000−i2i2−2200
χ562-22-22-22-2202i−2i2i−2i-2-200202i−2i000000000000−2i2i−2i2i-22-2200000000000−i2i2−i2i2000000−22−220000i2−i22−200
χ572-22-22-22-220−2i2i−2i2i-2-20020−2i2i0000000000002i−2i2i−2i-22-2200000000000i2−i2i2−i2000000−22−220000−i2i22−200
χ582-22-22-22-220−2i2i−2i2i-2-20020−2i2i0000000000002i−2i2i−2i-22-2200000000000−i2i2−i2i20000002−22−20000i2−i2−2200
χ592-22-22-22-220−2i2i−2i2i-2-20020−2i2i000000000000−2i2i−2i2i2-22-200000000000i2−i2i2−i2000000−22−220000i2−i2−2200
χ602-22-22-22-220−2i2i−2i2i-2-20020−2i2i000000000000−2i2i−2i2i2-22-200000000000−i2i2−i2i20000002−22−20000−i2i22−200
χ61444-4-4-4-444400004-4-44-4-40000-44000000000000000000000000000000000000000000000000000
χ62444-4-4-4-44-4-40000-444-4440000-44000000000000000000000000000000000000000000000000000
χ6344-4-444-4-4040000004-40-400000022−22−2222−222222−220000000000000000000000000000000000000000000
χ6444-4-444-4-4040000004-40-4000000−222222−2222−22−22220000000000000000000000000000000000000000000
χ6544-4-444-4-40-4000000-44040000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000000
χ6644-4-444-4-40-4000000-4404000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000000
χ674-444-44-4-4400000-4400-4000000000000000000000000000000000022−22−222200000000000000000000
χ684-444-44-4-4400000-4400-40000000000000000000000000000000000−222222−2200000000000000000000
χ694-444-44-4-4-4000004-4004000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ704-444-44-4-4-4000004-400400000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ714-44-44-44-4-404i−4i4i−4i4400-40−4i4i0000000000000000000000000000000000000000000000000000000
χ724-44-44-44-4-40−4i4i−4i4i4400-404i−4i0000000000000000000000000000000000000000000000000000000
χ734-4-4-4-4444004-4-440000000000000000000022−22−222222−22−222200000000000000000000000000000000000
χ744-4-4-4-4444004-4-4400000000000000000000−222222−22−222222−2200000000000000000000000000000000000
χ754-4-4-4-444400-444-40000000000000000000022−22−2222−222222−2200000000000000000000000000000000000
χ764-4-4-4-444400-444-400000000000000000000−222222−2222−22−222200000000000000000000000000000000000
χ778-8-888-8-88000000000000000000000000000000000000000000000000000000000000000000000

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