Finite Group Databasebeta

← Group #100319

Character table — Group #100319

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444222244444444448888888844444888888888888888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ911111111111-1-1-1-1-1-11-1-11111-1-1-111-1-1-1-1-1iiii−i−i−i−i111-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i11-1-11-1
χ1011111111111-1-1-1-1-1-11-1-11111-1-1-111-1-1-1-1-1iiii−i−i−i−i111-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iii-1-111-11
χ1111111111111-1-1-1-1-1-11-1-11111-1-1-111-1-1-1-1-1−i−i−i−iiiii111-1-1−i−iii−i−i−i−iiiiiiiii−i−i−i−iii−i−i-1-111-11
χ1211111111111-1-1-1-1-1-11-1-11111-1-1-111-1-1-1-1-1−i−i−i−iiiii111-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii11-1-11-1
χ1311111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1111111-1iiii−i−i−i−i1-1-111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii11-1-1-11
χ1411111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1111111-1iiii−i−i−i−i1-1-111ii−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-1111-1
χ1511111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1111111-1−i−i−i−iiiii1-1-111−i−iiiiiii−i−i−i−iiiii−i−i−i−i−i−iii-1-1111-1
χ1611111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1111111-1−i−i−i−iiiii1-1-111−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i11-1-1-11
χ172222222222222-2-2-222-22222222-2-2-22222-200000000-2-2-2-2-2000000000000000000000000000000
χ182222222222222-2-2-222-22-2-2-2-222-2-2-2-2-2-2-2-200000000-22222000000000000000000000000000000
χ1922222222222-2-2222-222-22222-2-22-2-2-2-2-2-2200000000-2-2-222000000000000000000000000000000
χ2022222222222-2-2222-222-2-2-2-2-2-2-22-2-22222200000000-222-2-2000000000000000000000000000000
χ2122222222-2-2-2222222-2220000-2-2-2220000-222222222-20000-2-2-2-200000000000000000000000000
χ2222222222-2-2-2222222-2220000-2-2-2220000-2-2-2-2-2-2-2-2-2-20000222200000000000000000000000000
χ2322222222-2-2-222-2-2-22-2-220000-2-22-2-2000020000000020000000022-2-222-2-2000000000000000000
χ2422222222-2-2-222-2-2-22-2-220000-2-22-2-20000200000000200000000-2-222-2-222000000000000000000
χ2522222222-2-2-2-2-2222-2-22-2000022-2-2-20000-2000000002000000002i2i−2i−2i−2i−2i2i2i000000000000000000
χ2622222222-2-2-2-2-2222-2-22-2000022-2-2-20000-200000000200000000−2i−2i2i2i2i2i−2i−2i000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2000022222000022i2i2i2i−2i−2i−2i−2i-20000−2i−2i2i2i00000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-200002222200002−2i−2i−2i−2i2i2i2i2i-200002i2i−2i−2i00000000000000000000000000
χ29222-2-22-2-222-222000-2-20-222-2-22-200022-2-20000000000000000000000000022−2−222−2−22−22−2000000
χ30222-2-22-2-222-222000-2-20-222-2-22-200022-2-200000000000000000000000000−2−222−2−222−22−22000000
χ31222-2-22-2-222-222000-2-20-2-2-2222-2000-2-2220000000000000000000000000022−2−222−2−2−22−22000000
χ32222-2-22-2-222-222000-2-20-2-2-2222-2000-2-22200000000000000000000000000−2−222−2−2222−22−2000000
χ33222-2-22-2-222-2-2-20002-20222-2-2-22000-2-22200000000000000000000000000i2i2−i2−i2−i2−i2i2i2i2−i2−i2i2000000
χ34222-2-22-2-222-2-2-20002-20222-2-2-22000-2-22200000000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2i2i2−i2000000
χ35222-2-22-2-222-2-2-20002-202-2-222-2200022-2-200000000000000000000000000i2i2−i2−i2−i2−i2i2i2−i2i2i2−i2000000
χ36222-2-22-2-222-2-2-20002-202-2-222-2200022-2-200000000000000000000000000−i2−i2i2i2i2i2−i2−i2i2−i2−i2i2000000
χ3722-22-2-2-222-220022-20-2-20000000-2002i−2i2i−2i2i2i2−i2−i2i2i2−i2−i202i−2i00i2−i2i2−i22−22−22−22−2000000000000000000
χ3822-22-2-2-222-220022-20-2-20000000-2002i−2i2i−2i2−i2−i2i2i2−i2−i2i2i202i−2i00−i2i2−i2i2−22−22−22−22000000000000000000
χ3922-22-2-2-222-220022-20-2-20000000-200−2i2i−2i2i2i2i2−i2−i2i2i2−i2−i20−2i2i00i2−i2i2−i2−22−22−22−22000000000000000000
χ4022-22-2-2-222-220022-20-2-20000000-200−2i2i−2i2i2−i2−i2i2i2−i2−i2i2i20−2i2i00−i2i2−i2i22−22−22−22−2000000000000000000
χ4122-22-2-2-222-2200-2-220-2200000002002i−2i2i−2i-222−2−2−2−2220−2i2i002−2−22i2−i2i2−i2−i2i2−i2i2000000000000000000
χ4222-22-2-2-222-2200-2-220-2200000002002i−2i2i−2i-2−2−22222−2−20−2i2i00−222−2−i2i2−i2i2i2−i2i2−i2000000000000000000
χ4322-22-2-2-222-2200-2-220-220000000200−2i2i−2i2i-222−2−2−2−22202i−2i002−2−22−i2i2−i2i2i2−i2i2−i2000000000000000000
χ4422-22-2-2-222-2200-2-220-220000000200−2i2i−2i2i-2−2−22222−2−202i−2i00−222−2i2−i2i2−i2−i2i2−i2i2000000000000000000
χ4522-22-2-2-22-22-20022-202-202-22-2002000000-2i2i2−i2−i2i2i2−i2−i20002-2−i2i2−i2i2i2−i2−i2i2−i2i2i2−i2000000000000000000
χ4622-22-2-2-22-22-20022-202-202-22-2002000000-2−i2−i2i2i2−i2−i2i2i20002-2i2−i2i2−i2−i2i2i2−i2i2−i2−i2i2000000000000000000
χ4722-22-2-2-22-22-20022-202-20-22-22002000000-2i2i2−i2−i2i2i2−i2−i2000-22−i2i2−i2i2−i2i2i2−i2i2−i2−i2i2000000000000000000
χ4822-22-2-2-22-22-20022-202-20-22-22002000000-2−i2−i2i2i2−i2−i2i2i2000-22i2−i2i2−i2i2−i2−i2i2−i2i2i2−i2000000000000000000
χ4922-22-2-2-22-22-200-2-2202202-22-200-2000000222−2−2−2−222000-22−222−22−2−222−2−22000000000000000000
χ5022-22-2-2-22-22-200-2-2202202-22-200-20000002−2−22222−2−2000-222−2−22−222−2−222−2000000000000000000
χ5122-22-2-2-22-22-200-2-220220-22-2200-2000000222−2−2−2−2220002-2−222−2−222−2−222−2000000000000000000
χ5222-22-2-2-22-22-200-2-220220-22-2200-20000002−2−22222−2−20002-22−2−222−2−222−2−22000000000000000000
χ532-2-2-2-22220002-22-2220-2-200000002-2000002i−2i2i−2i2i−2i2i−2i00000000000000000i2−i2i2−i2i2−i2i2−i200002−22−200
χ542-2-2-2-22220002-22-2220-2-200000002-2000002i−2i2i−2i2i−2i2i−2i00000000000000000−i2i2−i2i2−i2i2−i2i20000−22−2200
χ552-2-2-2-22220002-22-2220-2-200000002-200000−2i2i−2i2i−2i2i−2i2i00000000000000000i2−i2i2−i2i2−i2i2−i20000−22−2200
χ562-2-2-2-22220002-22-2220-2-200000002-200000−2i2i−2i2i−2i2i−2i2i00000000000000000−i2i2−i2i2−i2i2−i2i200002−22−200
χ572-2-2-2-2222000-22-22-2-202200000002-2000002-22-2-22-22000000000000000002−22−2−22−2200002−2−2200
χ582-2-2-2-2222000-22-22-2-202200000002-2000002-22-2-22-2200000000000000000−22−222−22−20000−222−200
χ592-2-2-2-2222000-22-22-2-202200000002-200000-22-222-22-2000000000000000002−22−2−22−220000−222−200
χ602-2-2-2-2222000-22-22-2-202200000002-200000-22-222-22-200000000000000000−22−222−22−200002−2−2200
χ61444-4-44-4-4-4-4444000-440-40000-44000000000000000000000000000000000000000000000000000
χ62444-4-44-4-4-4-44-4-4000440400004-4000000000000000000000000000000000000000000000000000
χ6344-4-44-44-44-4-40000004000000000004i−4i−4i4i00000000000000000000000000000000000000000000
χ6444-4-44-44-44-4-4000000400000000000−4i4i4i−4i00000000000000000000000000000000000000000000
χ6544-4-44-44-4-444000000-4004-4-4400000000000000000000000000000000000000000000000000000
χ6644-4-44-44-4-444000000-400-444-400000000000000000000000000000000000000000000000000000
χ674-44-44-4-44000004-4-400400000000000000022−22−222222−22−222200000000000000000000000000000000000
χ684-44-44-4-44000004-4-4004000000000000000−222222−22−222222−2200000000000000000000000000000000000
χ694-44-44-4-4400000-44400-40000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000
χ704-44-44-4-4400000-44400-4000000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000
χ714-4-4444-4-40004-4000-40040000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000
χ724-4-4444-4-40004-4000-4004000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000
χ734-4-4444-4-4000-44000400-40000000000000000000000000000000000000002-2-22-222-20000000000
χ744-4-4444-4-4000-44000400-4000000000000000000000000000000000000000-222-22-2-220000000000
χ754-4-4-4-44440004-4-44-4404-40000000-44000000000000000000000000000000000000000000000000
χ764-4-4-4-4444000-444-44-40-440000000-44000000000000000000000000000000000000000000000000
χ778-888-8-88-8000000000000000000000000000000000000000000000000000000000000000000000

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