Finite Group Databasebeta

← Group #101728

Character table — Group #101728

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444888888888888888822224444488888888888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
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
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−iiiii−i−i−i−i11-1-1-111-1-1ii−i−iii−i−i1111-1-1-1-1ii−i−iii−i−i1-1
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−iiiii−i−i−i−i11-1-1-111-1-1ii−i−iii−i−i-1-1-1-11111−i−iii−i−iii-11
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-1-111ii−i−i−i−iii1111-1-1-1-1ii−i−i−i−iii-11
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-1-111ii−i−i−i−iii-1-1-1-11111−i−iiiii−i−i1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1-111−i−iiiii−i−i1111-1-1-1-1−i−iiiii−i−i-11
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1-111−i−iiiii−i−i-1-1-1-11111ii−i−i−i−iii1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiii−i−i−i−iiiii11-1-1-111-1-1−i−iii−i−iii1111-1-1-1-1−i−iii−i−iii1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1111111−i−i−i−iiiii−i−i−i−iiiii11-1-1-111-1-1−i−iii−i−iii-1-1-1-11111ii−i−iii−i−i-11
χ1722222222222222-2-2-222-2-2-2-2-22200000000000000002222-2-2-2-2-200000000000000000000000000
χ1822222222222222-2-2-222-2-2-2-2-2220000000000000000-2-2-2-2-2222200000000000000000000000000
χ1922222222222-2-2-22222-2222-2-2-2-200000000222222220000-200000000-2-2-2-2000000000000000000
χ2022222222222-2-2-22222-2222-2-2-2-200000000-2-2-2-2-2-2-2-20000-2000000002222000000000000000000
χ2122222222222-2-2-2-2-2-22-2-2-2-222-2-22i2i2i2i−2i−2i−2i−2i00000000000020000−2i−2i2i2i0000000000000000000000
χ2222222222222-2-2-2-2-2-22-2-2-2-222-2-2−2i−2i−2i−2i2i2i2i2i000000000000200002i2i−2i−2i0000000000000000000000
χ2322222222-2-2-2222222-222-2-222-2-222222222000000000000-20000-2-2-2-20000000000000000000000
χ2422222222-2-2-2222222-222-2-222-2-2-2-2-2-2-2-2-2-2000000000000-2000022220000000000000000000000
χ2522222222-2-2-2222-2-2-2-22-222-2-2-2-2000000002i2i2i2i−2i−2i−2i−2i0000200000000−2i−2i2i2i000000000000000000
χ2622222222-2-2-2222-2-2-2-22-222-2-2-2-200000000−2i−2i−2i−2i2i2i2i2i00002000000002i2i−2i−2i000000000000000000
χ2722222222-2-2-2-2-2-2222-2-22-2-2-2-222000000000000000022-2-22-2-22200000000000000000000000000
χ2822222222-2-2-2-2-2-2222-2-22-2-2-2-2220000000000000000-2-222222-2-200000000000000000000000000
χ29222-2-2-22-200022-2-22-20-22002-20022-2-222-2-20000000000000000000000000i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2000000
χ30222-2-2-22-200022-2-22-20-22002-20022-2-222-2-20000000000000000000000000−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2000000
χ31222-2-2-22-200022-2-22-20-22002-200-2-222-2-2220000000000000000000000000i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2000000
χ32222-2-2-22-200022-2-22-20-22002-200-2-222-2-2220000000000000000000000000−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2000000
χ33222-2-2-22-2000-2-222-2202-2002-2002i2i−2i−2i−2i−2i2i2i0000000000000000000000000i2i2−i2−i2−i2−i2i2i2−222−2000000
χ34222-2-2-22-2000-2-222-2202-2002-2002i2i−2i−2i−2i−2i2i2i0000000000000000000000000−i2−i2i2i2i2i2−i2−i22−2−22000000
χ35222-2-2-22-2000-2-222-2202-2002-200−2i−2i2i2i2i2i−2i−2i0000000000000000000000000i2i2−i2−i2−i2−i2i2i22−2−22000000
χ36222-2-2-22-2000-2-222-2202-2002-200−2i−2i2i2i2i2i−2i−2i0000000000000000000000000−i2−i2i2i2i2i2−i2−i2−222−2000000
χ3722-22-2-2-2222-22-22000-2-200000-22i2−i2i2−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2−i22-22-200000i2−i2i2−i2i2−i2i2−i2000000000000000000
χ3822-22-2-2-2222-22-22000-2-200000-22i2−i2i2−i2i2−i2i2−i2−i2−i2i2i2−i2−i2i2i2-22-2200000i2−i2i2−i2−i2i2−i2i2000000000000000000
χ3922-22-2-2-2222-22-22000-2-200000-22−i2i2−i2i2−i2i2−i2i2i2i2−i2−i2i2i2−i2−i2-22-2200000−i2i2−i2i2i2−i2i2−i2000000000000000000
χ4022-22-2-2-2222-22-22000-2-200000-22−i2i2−i2i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2i22-22-200000−i2i2−i2i2−i2i2−i2i2000000000000000000
χ4122-22-2-2-2222-2-22-2000-22000002-22−22−2−22−22i2i2−i2−i2i2i2−i2−i2000002i−2i2i−2i−222−2−i2i2−i2i2000000000000000000
χ4222-22-2-2-2222-2-22-2000-22000002-22−22−2−22−22−i2−i2i2i2−i2−i2i2i200000−2i2i−2i2i−222−2i2−i2i2−i2000000000000000000
χ4322-22-2-2-2222-2-22-2000-22000002-2−22−222−22−2i2i2−i2−i2i2i2−i2−i200000−2i2i−2i2i2−2−22−i2i2−i2i2000000000000000000
χ4422-22-2-2-2222-2-22-2000-22000002-2−22−222−22−2−i2−i2i2i2−i2−i2i2i2000002i−2i2i−2i2−2−22i2−i2i2−i2000000000000000000
χ4522-22-2-2-22-2-222-220002-2000002-2i2−i2i2−i2i2−i2i2−i222−2−2−2−22200000−2i2i2i−2i−i2i2−i2i2−222−2000000000000000000
χ4622-22-2-2-22-2-222-220002-2000002-2i2−i2i2−i2i2−i2i2−i2−2−22222−2−2000002i−2i−2i2i−i2i2−i2i22−2−22000000000000000000
χ4722-22-2-2-22-2-222-220002-2000002-2−i2i2−i2i2−i2i2−i2i222−2−2−2−222000002i−2i−2i2ii2−i2i2−i2−222−2000000000000000000
χ4822-22-2-2-22-2-222-220002-2000002-2−i2i2−i2i2−i2i2−i2i2−2−22222−2−200000−2i2i2i−2ii2−i2i2−i22−2−22000000000000000000
χ4922-22-2-2-22-2-22-22-20002200000-222−22−2−22−2222−2−2−2−2222-2-22000002−2−222−2−22000000000000000000
χ5022-22-2-2-22-2-22-22-20002200000-222−22−2−22−22−2−22222−2−2-222-2000002−2−22−222−2000000000000000000
χ5122-22-2-2-22-2-22-22-20002200000-22−22−222−22−222−2−2−2−222-222-200000−222−22−2−22000000000000000000
χ5222-22-2-2-22-2-22-22-20002200000-22−22−222−22−2−2−22222−2−22-2-2200000−222−2−222−2000000000000000000
χ532-2-222-22-22-22000-2-22-2022-20000000000002-22-22-22-200000000000000000i2−i2i2−i2i2−i2i2−i20000i2−i2i2−i200
χ542-2-222-22-22-22000-2-22-2022-20000000000002-22-22-22-200000000000000000−i2i2−i2i2−i2i2−i2i20000−i2i2−i2i200
χ552-2-222-22-22-22000-2-22-2022-2000000000000-22-22-22-2200000000000000000i2−i2i2−i2i2−i2i2−i20000−i2i2−i2i200
χ562-2-222-22-22-22000-2-22-2022-2000000000000-22-22-22-2200000000000000000−i2i2−i2i2−i2i2−i2i20000i2−i2i2−i200
χ572-2-222-22-2-22-200022-220-22-20000000000002i−2i2i−2i−2i2i−2i2i00000000000000000i2−i2i2−i2−i2i2−i2i20000−222−200
χ582-2-222-22-2-22-200022-220-22-20000000000002i−2i2i−2i−2i2i−2i2i00000000000000000−i2i2−i2i2i2−i2i2−i200002−2−2200
χ592-2-222-22-2-22-200022-220-22-2000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000i2−i2i2−i2−i2i2−i2i200002−2−2200
χ602-2-222-22-2-22-200022-220-22-2000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000−i2i2−i2i2i2−i2i2−i20000−222−200
χ61444-4-4-44-400044-44-440-4-400-4400000000000000000000000000000000000000000000000000000
χ62444-4-4-44-4000-4-44-44-404400-4400000000000000000000000000000000000000000000000000000
χ6344-4-444-4-40004-4-40000400000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000000
χ6444-4-444-4-40004-4-4000040000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000000
χ6544-4-444-4-4000-4440000-4000000022−22−2222−222222−220000000000000000000000000000000000000000000
χ6644-4-444-4-4000-4440000-40000000−222222−2222−22−22220000000000000000000000000000000000000000000
χ674-444-44-4-44-4-4000000400000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ684-444-44-4-44-4-400000040000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ694-444-44-4-4-444000000-4000000000000000022−22−2222−222222−2200000000000000000000000000000000000
χ704-444-44-4-4-444000000-40000000000000000−222222−2222−22−222200000000000000000000000000000000000
χ714-4-444-44-44-4400044-4-40-4-440000000000000000000000000000000000000000000000000000000
χ724-4-444-44-4-44-4000-4-44404-440000000000000000000000000000000000000000000000000000000
χ734-4-4-4-44440000004-4-40040000000000000000000000000000000000000002-2-222-2-220000000000
χ744-4-4-4-44440000004-4-4004000000000000000000000000000000000000000-222-2-222-20000000000
χ754-4-4-4-4444000000-44400-40000000000000000000000000000000000000002-2-22-222-20000000000
χ764-4-4-4-4444000000-44400-4000000000000000000000000000000000000000-222-22-2-220000000000
χ778-88-88-8-88000000000000000000000000000000000000000000000000000000000000000000000

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