Finite Group Databasebeta

← Group #101718

Character table — Group #101718

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444888888888888888844444444488888888888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
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−i-11111-1-1-1-1ii−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−i-11111-1-1-1-1ii−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-1-1-1-1-11111ii−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-1-1-1-1-11111ii−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-1-1-1-1-11111−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-1-1-1-1-11111−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−iiiii-11111-1-1-1-1−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−iiiii-11111-1-1-1-1−i−iii−i−iii-1-1-1-11111ii−i−iii−i−i-11
χ17222222222222-2-2-22222-222-2-2-2-20000000022222222-2000000000000-2-2-2-2000000000000000000
χ18222222222222-2-2-22222-222-2-2-2-200000000-2-2-2-2-2-2-2-2-20000000000002222000000000000000000
χ1922222222222-2222-2-22-22-2-2-2-2220000000000000000-222-2-222-2-200000000000000000000000000
χ2022222222222-2222-2-22-22-2-2-2-2220000000000000000-2-2-222-2-22200000000000000000000000000
χ2122222222222-2-2-2-2-2-22-2-2-2-222-2-22i2i2i2i−2i−2i−2i−2i00000000200000000−2i−2i2i2i0000000000000000000000
χ2222222222222-2-2-2-2-2-22-2-2-2-222-2-2−2i−2i−2i−2i2i2i2i2i000000002000000002i2i−2i−2i0000000000000000000000
χ2322222222-2-2-2222222-222-2-222-2-22222222200000000-200000000-2-2-2-20000000000000000000000
χ2422222222-2-2-2222222-222-2-222-2-2-2-2-2-2-2-2-2-200000000-20000000022220000000000000000000000
χ2522222222-2-2-22-2-2-222-22-2-2-2-2-2220000000000000000222-2-2-2-22200000000000000000000000000
χ2622222222-2-2-22-2-2-222-22-2-2-2-2-22200000000000000002-2-22222-2-200000000000000000000000000
χ2722222222-2-2-2-2222-2-2-2-2222-2-2-2-2000000002i2i2i2i−2i−2i−2i−2i2000000000000−2i−2i2i2i000000000000000000
χ2822222222-2-2-2-2222-2-2-2-2222-2-2-2-200000000−2i−2i−2i−2i2i2i2i2i20000000000002i2i−2i−2i000000000000000000
χ292222-2-2-2-222-220002-2-2-202-200000000000022-2-222-2-20000000000000000022−2−222−2−200002−22−200
χ302222-2-2-2-222-220002-2-2-202-200000000000022-2-222-2-200000000000000000−2−222−2−2220000−22−2200
χ312222-2-2-2-222-220002-2-2-202-2000000000000-2-222-2-2220000000000000000022−2−222−2−20000−22−2200
χ322222-2-2-2-222-220002-2-2-202-2000000000000-2-222-2-22200000000000000000−2−222−2−22200002−22−200
χ332222-2-2-2-2-2-22-2000-222202-20000000000002i2i−2i−2i−2i−2i2i2i0000000000000000022−2−2−2−2220000i2−i2−i2i200
χ342222-2-2-2-2-2-22-2000-222202-20000000000002i2i−2i−2i−2i−2i2i2i00000000000000000−2−22222−2−20000−i2i2i2−i200
χ352222-2-2-2-2-2-22-2000-222202-2000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000022−2−2−2−2220000−i2i2i2−i200
χ362222-2-2-2-2-2-22-2000-222202-2000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000−2−22222−2−20000i2−i2−i2i200
χ3722-2-22-2-2200022-2-2-220-22002-20022-2-222-2-20000000000000000000000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000
χ3822-2-22-2-2200022-2-2-220-22002-20022-2-222-2-20000000000000000000000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000
χ3922-2-22-2-2200022-2-2-220-22002-200-2-222-2-2220000000000000000000000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000
χ4022-2-22-2-2200022-2-2-220-22002-200-2-222-2-2220000000000000000000000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000
χ4122-2-22-2-22000-2-2222-202-2002-2002i2i−2i−2i−2i−2i2i2i0000000000000000000000000i2−i2i2−i2−i2i2−i2i2−222−2000000
χ4222-2-22-2-22000-2-2222-202-2002-2002i2i−2i−2i−2i−2i2i2i0000000000000000000000000−i2i2−i2i2i2−i2i2−i22−2−22000000
χ4322-2-22-2-22000-2-2222-202-2002-200−2i−2i2i2i2i2i−2i−2i0000000000000000000000000i2−i2i2−i2−i2i2−i2i22−2−22000000
χ4422-2-22-2-22000-2-2222-202-2002-200−2i−2i2i2i2i2i−2i−2i0000000000000000000000000−i2i2−i2i2i2−i2i2−i2−222−2000000
χ452-22-2-22-222-22022-200-20-20000-22i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20002-2002-2i2−i2i2−i2i2−i2i2−i2000000000000000000
χ462-22-2-22-222-22022-200-20-20000-22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000-2200-22i2−i2i2−i2−i2i2−i2i2000000000000000000
χ472-22-2-22-222-22022-200-20-20000-22−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000-2200-22−i2i2−i2i2i2−i2i2−i2000000000000000000
χ482-22-2-22-222-22022-200-20-20000-22−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20002-2002-2−i2i2−i2i2−i2i2−i2i2000000000000000000
χ492-22-2-22-222-220-2-2200-20200002-22−22−2−22−22i2−i2i2−i2i2−i2i2−i202i−2i002i−2i00−222−2−i2i2−i2i2000000000000000000
χ502-22-2-22-222-220-2-2200-20200002-22−22−2−22−22−i2i2−i2i2−i2i2−i2i20−2i2i00−2i2i00−222−2i2−i2i2−i2000000000000000000
χ512-22-2-22-222-220-2-2200-20200002-2−22−222−22−2i2−i2i2−i2i2−i2i2−i20−2i2i00−2i2i002−2−22−i2i2−i2i2000000000000000000
χ522-22-2-22-222-220-2-2200-20200002-2−22−222−22−2−i2i2−i2i2−i2i2−i2i202i−2i002i−2i002−2−22i2−i2i2−i2000000000000000000
χ532-22-2-22-22-22-2022-20020-200002-2i2−i2i2−i2i2−i2i2−i22−22−2−22−220−2i2i002i−2i00−i2i2−i2i2−222−2000000000000000000
χ542-22-2-22-22-22-2022-20020-200002-2i2−i2i2−i2i2−i2i2−i2−22−222−22−202i−2i00−2i2i00−i2i2−i2i22−2−22000000000000000000
χ552-22-2-22-22-22-2022-20020-200002-2−i2i2−i2i2−i2i2−i2i22−22−2−22−2202i−2i00−2i2i00i2−i2i2−i2−222−2000000000000000000
χ562-22-2-22-22-22-2022-20020-200002-2−i2i2−i2i2−i2i2−i2i2−22−222−22−20−2i2i002i−2i00i2−i2i2−i22−2−22000000000000000000
χ572-22-2-22-22-22-20-2-22002020000-222−22−2−22−222−22−2−22−220002-200-222−2−222−2−22000000000000000000
χ582-22-2-22-22-22-20-2-22002020000-222−22−2−22−22−22−222−22−2000-22002-22−2−22−222−2000000000000000000
χ592-22-2-22-22-22-20-2-22002020000-22−22−222−22−22−22−2−22−22000-22002-2−222−22−2−22000000000000000000
χ602-22-2-22-22-22-20-2-22002020000-22−22−222−22−2−22−222−22−20002-200-22−222−2−222−2000000000000000000
χ614444-4-4-4-444-4-4000-44-440-440000000000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4-4440004-44-40-440000000000000000000000000000000000000000000000000000000
χ6344-4-44-4-440004-444-440-4-400-4400000000000000000000000000000000000000000000000000000
χ6444-4-44-4-44000-44-4-44-404400-4400000000000000000000000000000000000000000000000000000
χ6544-4-4-444-40004000-4-40400000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000
χ6644-4-4-444-40004000-4-4040000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000
χ6744-4-4-444-4000-4000440-400000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000
χ6844-4-4-444-4000-4000440-40000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000
χ694-44-44-44-44-4-4000000400000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ704-44-44-44-44-4-400000040000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ714-44-44-44-4-444000000-4000000000000000022−22−2222−222222−2200000000000000000000000000000000000
χ724-44-44-44-4-444000000-40000000000000000−222222−2222−22−222200000000000000000000000000000000000
χ734-4-44-4-44400004-440000-40000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000000
χ744-4-44-4-44400004-440000-4000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000000
χ754-4-44-4-4440000-44-40000400000022−22−2222−222222−220000000000000000000000000000000000000000000
χ764-4-44-4-4440000-44-400004000000−222222−2222−22−22220000000000000000000000000000000000000000000
χ778-8-8888-8-8000000000000000000000000000000000000000000000000000000000000000000000

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