Finite Group Databasebeta

← Group #316784

Character table — Group #316784

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222444444444444888888884444444488888888888844444444888888882244444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ1111111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ1311111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ1411111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ1511111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ17222222222222222-2-2-2-222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ18222222222222222-2-2-2-22-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ19222222222222-2-2-22222-200000000-2-2-2-2-2-22200000000000022-2-2-2-222000000000000000000000000
χ20222222222222-2-2-22222-200000000-2-2-2-2-2-222000000000000-2-22222-2-2000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-200000000-2-22222-2-2000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ22222222222222-2-2-2-2-2-2-2-200000000-2-22222-2-200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222222-2-2-2-2222-2-2-2-2222222222-2-222-2-222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2422222222-2-2-2-2222-2-2-2-22-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2-2-2222200000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-22222-2000000002222-2-2-2-20000000000002222-2-2-2-2000000000000000000000000
χ2622222222-2-2-2-2-2-2-22222-2000000002222-2-2-2-2000000000000-2-2-2-22222000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-22222000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-2222200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ29222-22-2-2-222-2-22-2-2000022i2i2i2i−2i−2i−2i−2i2-20000002i2i−2i−2i00000000000000000000000000000000i2−i2i2−i22−22−2
χ30222-22-2-2-222-2-22-2-2000022i2i2i2i−2i−2i−2i−2i2-20000002i2i−2i−2i00000000000000000000000000000000−i2i2−i2i2−22−22
χ31222-22-2-2-222-2-22-2-200002−2i−2i−2i−2i2i2i2i2i2-2000000−2i−2i2i2i00000000000000000000000000000000i2−i2i2−i2−22−22
χ32222-22-2-2-222-2-22-2-200002−2i−2i−2i−2i2i2i2i2i2-2000000−2i−2i2i2i00000000000000000000000000000000−i2i2−i2i22−22−2
χ33222-22-2-2-2-2-2222-2-2000022i2i2i2i−2i−2i−2i−2i-22000000−2i−2i2i2i00000000000000000000000000000000i2−i2−i2i22−2−22
χ34222-22-2-2-2-2-2222-2-2000022i2i2i2i−2i−2i−2i−2i-22000000−2i−2i2i2i00000000000000000000000000000000−i2i2i2−i2−222−2
χ35222-22-2-2-2-2-2222-2-200002−2i−2i−2i−2i2i2i2i2i-220000002i2i−2i−2i00000000000000000000000000000000i2−i2−i2i2−222−2
χ36222-22-2-2-2-2-2222-2-200002−2i−2i−2i−2i2i2i2i2i-220000002i2i−2i−2i00000000000000000000000000000000−i2i2i2−i22−2−22
χ3722-22-2-2-222i−2i2i−2i00022-2-20i2i2−i2−i2i2i2−i2−i20000002i−2i2−22−222−2−2i2i2−i2−i2002i−2i2-200i2−i2i2−i22−22−20000000000000000
χ3822-22-2-2-222i−2i2i−2i00022-2-20i2i2−i2−i2i2i2−i2−i20000002i−2i2−22−222−2−2i2i2−i2−i200−2i2i-2200−i2i2−i2i2−22−220000000000000000
χ3922-22-2-2-222i−2i2i−2i00022-2-20−i2−i2i2i2−i2−i2i2i20000002i−2i−22−22−2−222−i2−i2i2i2002i−2i2-200−i2i2−i2i2−22−220000000000000000
χ4022-22-2-2-222i−2i2i−2i00022-2-20−i2−i2i2i2−i2−i2i2i20000002i−2i−22−22−2−222−i2−i2i2i200−2i2i-2200i2−i2i2−i22−22−20000000000000000
χ4122-22-2-2-222i−2i2i−2i000-2-2220i2i2−i2−i2i2i2−i2−i2000000−2i2i2−22−2−2−222−i2−i2i2i22i−2i00002-22−2−22−i2i2i2−i20000000000000000
χ4222-22-2-2-222i−2i2i−2i000-2-2220i2i2−i2−i2i2i2−i2−i2000000−2i2i2−22−2−2−222−i2−i2i2i2−2i2i0000-22−222−2i2−i2−i2i20000000000000000
χ4322-22-2-2-222i−2i2i−2i000-2-2220−i2−i2i2i2−i2−i2i2i2000000−2i2i−22−2222−2−2i2i2−i2−i22i−2i00002-2−222−2i2−i2−i2i20000000000000000
χ4422-22-2-2-222i−2i2i−2i000-2-2220−i2−i2i2i2−i2−i2i2i2000000−2i2i−22−2222−2−2i2i2−i2−i2−2i2i0000-222−2−22−i2i2i2−i20000000000000000
χ4522-22-2-2-22−2i2i−2i2i00022-2-20i2i2−i2−i2i2i2−i2−i2000000−2i2i−22−22−2−222i2i2−i2−i2002i−2i-2200−i2i2−i2i22−22−20000000000000000
χ4622-22-2-2-22−2i2i−2i2i00022-2-20i2i2−i2−i2i2i2−i2−i2000000−2i2i−22−22−2−222i2i2−i2−i200−2i2i2-200i2−i2i2−i2−22−220000000000000000
χ4722-22-2-2-22−2i2i−2i2i00022-2-20−i2−i2i2i2−i2−i2i2i2000000−2i2i2−22−222−2−2−i2−i2i2i2002i−2i-2200i2−i2i2−i2−22−220000000000000000
χ4822-22-2-2-22−2i2i−2i2i00022-2-20−i2−i2i2i2−i2−i2i2i2000000−2i2i2−22−222−2−2−i2−i2i2i200−2i2i2-200−i2i2−i2i22−22−20000000000000000
χ4922-22-2-2-22−2i2i−2i2i000-2-2220i2i2−i2−i2i2i2−i2−i20000002i−2i−22−2222−2−2−i2−i2i2i22i−2i0000-222−2−22i2−i2−i2i20000000000000000
χ5022-22-2-2-22−2i2i−2i2i000-2-2220i2i2−i2−i2i2i2−i2−i20000002i−2i−22−2222−2−2−i2−i2i2i2−2i2i00002-2−222−2−i2i2i2−i20000000000000000
χ5122-22-2-2-22−2i2i−2i2i000-2-2220−i2−i2i2i2−i2−i2i2i20000002i−2i2−22−2−2−222i2i2−i2−i22i−2i0000-22−222−2−i2i2i2−i20000000000000000
χ5222-22-2-2-22−2i2i−2i2i000-2-2220−i2−i2i2i2−i2−i2i2i20000002i−2i2−22−2−2−222i2i2−i2−i2−2i2i00002-22−2−22i2−i2−i2i20000000000000000
χ532-22-2-22-22000022-22-22-2-22i−2i2i−2i2i−2i2i−2i00002-200000000002i−2i2i−2i0000000000000000002i−2i002-200000000
χ542-22-2-22-22000022-22-22-2-22i−2i2i−2i2i−2i2i−2i00002-200000000002i−2i2i−2i000000000000000000−2i2i00-2200000000
χ552-22-2-22-22000022-22-22-2-2−2i2i−2i2i−2i2i−2i2i00002-20000000000−2i2i−2i2i0000000000000000002i−2i00-2200000000
χ562-22-2-22-22000022-22-22-2-2−2i2i−2i2i−2i2i−2i2i00002-20000000000−2i2i−2i2i000000000000000000−2i2i002-200000000
χ572-22-2-22-22000022-2-22-22-22i−2i2i−2i2i−2i2i−2i0000-220000000000−2i2i−2i2i00000000000000002-2002i−2i0000000000
χ582-22-2-22-22000022-2-22-22-22i−2i2i−2i2i−2i2i−2i0000-220000000000−2i2i−2i2i0000000000000000-2200−2i2i0000000000
χ592-22-2-22-22000022-2-22-22-2−2i2i−2i2i−2i2i−2i2i0000-2200000000002i−2i2i−2i00000000000000002-200−2i2i0000000000
χ602-22-2-22-22000022-2-22-22-2−2i2i−2i2i−2i2i−2i2i0000-2200000000002i−2i2i−2i0000000000000000-22002i−2i0000000000
χ61444-44-4-4-444-4-4-4440000-400000000-4400000000000000000000000000000000000000000000000000
χ62444-44-4-4-4-4-444-4440000-4000000004-400000000000000000000000000000000000000000000000000
χ6344-4-4-444-44i−4i−4i4i000000002222−22−22−22−22222200000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ6444-4-4-444-44i−4i−4i4i00000000−22−2222222222−22−22000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ6544-4-4-444-4−4i4i4i−4i000000002222−22−22−22−222222000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ6644-4-4-444-4−4i4i4i−4i00000000−22−2222222222−22−2200000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ674-444-4-44-400004-440000-44-44-4-44-440000000000000000000000000000000000000000000000000000
χ684-444-4-44-400004-440000-4-44-444-44-40000000000000000000000000000000000000000000000000000
χ694-444-4-44-40000-44-400004000000000000000000004i−4i4i−4i000000000000000000000000000000000000
χ704-444-4-44-40000-44-40000400000000000000000000−4i4i−4i4i000000000000000000000000000000000000
χ714-44-4-44-440000-4-444-44-44000000000000-440000000000000000000000000000000000000000000000
χ724-44-4-44-440000-4-44-44-4440000000000004-40000000000000000000000000000000000000000000000
χ734-4-4444-4-40000000000002i2−2i2−2i22i2−2i22i22i2−2i2004-4000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ744-4-4444-4-40000000000002i2−2i2−2i22i2−2i22i22i2−2i200-4400000000−2i22i22i2−2i2000000000000000000000000000000000000
χ754-4-4444-4-4000000000000−2i22i22i2−2i22i2−2i2−2i22i2004-400000000−2i22i22i2−2i2000000000000000000000000000000000000
χ764-4-4444-4-4000000000000−2i22i22i2−2i22i2−2i2−2i22i200-44000000002i2−2i2−2i22i2000000000000000000000000000000000000
χ774-4-4-44-44400000004-4-44022−22−222222−22−2222000000000000000022−22−222200000000000000000000000000000000
χ784-4-4-44-44400000004-4-440−222222−22−222222−220000000000000000−222222−2200000000000000000000000000000000
χ794-4-4-44-4440000000-444-4022−22−222222−22−22220000000000000000−222222−2200000000000000000000000000000000
χ804-4-4-44-4440000000-444-40−222222−22−222222−22000000000000000022−22−222200000000000000000000000000000000

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