Finite Group Databasebeta

← Group #98921

Character table — Group #98921

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222244444444888888884444444488888888888844444444888888884444444488888888
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
χ911111111-1-1-1-1111-1-1-1-1111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1111-1-1-1-1111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-1-1-1111-1-1-1-1111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-1-1-1111-1-1-1-1111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-1111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
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
χ19222222222222-2-2-22222-200000000-2-222-2-2-2-200000000000022-2-222-2-2000000000000000000000000
χ20222222222222-2-2-22222-200000000-2-222-2-2-2-2000000000000-2-222-2-222000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-200000000-2-2-2-22222000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ22222222222222-2-2-2-2-2-2-2-200000000-2-2-2-2222200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222222-2-2-2-22222222222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ2422222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-200000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-22222-20000000022-2-222-2-2000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2622222222-2-2-2-2-2-2-22222-20000000022-2-222-2-200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-22200000000000022-2-2-2-222000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222-2-222000000000000-2-22222-2-2000000000000000000000000
χ292222-2-2-2-222-2-222-20000-22222-2-2-2-22-200000022-2-2000000000000000000000000000000002−22−22−22−2
χ302222-2-2-2-222-2-222-20000-22222-2-2-2-22-200000022-2-200000000000000000000000000000000−22−22−22−22
χ312222-2-2-2-222-2-222-20000-2-2-2-2-222222-2000000-2-222000000000000000000000000000000002−22−2−22−22
χ322222-2-2-2-222-2-222-20000-2-2-2-2-222222-2000000-2-22200000000000000000000000000000000−22−222−22−2
χ332222-2-2-2-2-2-22222-20000-22222-2-2-2-2-22000000-2-22200000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ342222-2-2-2-2-2-22222-20000-22222-2-2-2-2-22000000-2-22200000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ352222-2-2-2-2-2-22222-20000-2-2-2-2-22222-2200000022-2-200000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ362222-2-2-2-2-2-22222-20000-2-2-2-2-22222-2200000022-2-200000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ3722-2-22-22-22-22-200022-2-20i2i2−i2−i2i2i2−i2−i2002-20000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i2002i−2i002i−2i2−22−22−22−20000000000000000
χ3822-2-22-22-22-22-200022-2-20i2i2−i2−i2i2i2−i2−i2002-20000i2−i2i2−i2i2i2−i2−i2i2i2−i2−i200−2i2i00−2i2i−22−22−22−220000000000000000
χ3922-2-22-22-22-22-200022-2-20−i2−i2i2i2−i2−i2i2i2002-20000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i2002i−2i002i−2i−22−22−22−220000000000000000
χ4022-2-22-22-22-22-200022-2-20−i2−i2i2i2−i2−i2i2i2002-20000−i2i2−i2i2−i2−i2i2i2−i2−i2i2i200−2i2i00−2i2i2−22−22−22−20000000000000000
χ4122-2-22-22-22-22-2000-2-2220i2i2−i2−i2i2i2−i2−i200-220000i2−i2i2−i2−i2−i2i2i2−i2−i2i2i22-2002-200i2−i2−i2i2i2−i2−i2i20000000000000000
χ4222-2-22-22-22-22-2000-2-2220i2i2−i2−i2i2i2−i2−i200-220000i2−i2i2−i2−i2−i2i2i2−i2−i2i2i2-2200-2200−i2i2i2−i2−i2i2i2−i20000000000000000
χ4322-2-22-22-22-22-2000-2-2220−i2−i2i2i2−i2−i2i2i200-220000−i2i2−i2i2i2i2−i2−i2i2i2−i2−i22-2002-200−i2i2i2−i2−i2i2i2−i20000000000000000
χ4422-2-22-22-22-22-2000-2-2220−i2−i2i2i2−i2−i2i2i200-220000−i2i2−i2i2i2i2−i2−i2i2i2−i2−i2-2200-2200i2−i2−i2i2i2−i2−i2i20000000000000000
χ4522-2-22-22-2-22-2200022-2-20i2i2−i2−i2i2i2−i2−i200-220000−i2i2−i2i2−i2−i2i2i2i2i2−i2−i22-200-2200i2−i2−i2i2−i2i2i2−i20000000000000000
χ4622-2-22-22-2-22-2200022-2-20i2i2−i2−i2i2i2−i2−i200-220000−i2i2−i2i2−i2−i2i2i2i2i2−i2−i2-22002-200−i2i2i2−i2i2−i2−i2i20000000000000000
χ4722-2-22-22-2-22-2200022-2-20−i2−i2i2i2−i2−i2i2i200-220000i2−i2i2−i2i2i2−i2−i2−i2−i2i2i22-200-2200−i2i2i2−i2i2−i2−i2i20000000000000000
χ4822-2-22-22-2-22-2200022-2-20−i2−i2i2i2−i2−i2i2i200-220000i2−i2i2−i2i2i2−i2−i2−i2−i2i2i2-22002-200i2−i2−i2i2−i2i2i2−i20000000000000000
χ4922-2-22-22-2-22-22000-2-2220i2i2−i2−i2i2i2−i2−i2002-20000−i2i2−i2i2i2i2−i2−i2−i2−i2i2i2002i−2i00−2i2i2−22−2−22−220000000000000000
χ5022-2-22-22-2-22-22000-2-2220i2i2−i2−i2i2i2−i2−i2002-20000−i2i2−i2i2i2i2−i2−i2−i2−i2i2i200−2i2i002i−2i−22−222−22−20000000000000000
χ5122-2-22-22-2-22-22000-2-2220−i2−i2i2i2−i2−i2i2i2002-20000i2−i2i2−i2−i2−i2i2i2i2i2−i2−i2002i−2i00−2i2i−22−222−22−20000000000000000
χ5222-2-22-22-2-22-22000-2-2220−i2−i2i2i2−i2−i2i2i2002-20000i2−i2i2−i2−i2−i2i2i2i2i2−i2−i200−2i2i002i−2i2−22−2−22−220000000000000000
χ532-2-2222-2-20000-2222i−2i2i−2i-22-22-22-22-20000002i−2i000000002i−2i2i−2i00000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ542-2-2222-2-20000-2222i−2i2i−2i-22-22-22-22-20000002i−2i000000002i−2i2i−2i0000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ552-2-2222-2-20000-2222i−2i2i−2i-2-22-22-22-220000002i−2i00000000−2i2i−2i2i00000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000
χ562-2-2222-2-20000-2222i−2i2i−2i-2-22-22-22-220000002i−2i00000000−2i2i−2i2i0000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i00000000
χ572-2-2222-2-20000-222−2i2i−2i2i-22-22-22-22-2000000−2i2i00000000−2i2i−2i2i00000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ582-2-2222-2-20000-222−2i2i−2i2i-22-22-22-22-2000000−2i2i00000000−2i2i−2i2i0000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ592-2-2222-2-20000-222−2i2i−2i2i-2-22-22-22-22000000−2i2i000000002i−2i2i−2i00000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000
χ602-2-2222-2-20000-222−2i2i−2i2i-2-22-22-22-22000000−2i2i000000002i−2i2i−2i0000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000
χ614444-4-4-4-444-4-4-4-440000400000000-4400000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4-444-4-4400004000000004-400000000000000000000000000000000000000000000000000
χ6344-4-4-44-444-4-44000000002i22i2−2i2−2i2−2i2−2i22i22i2000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ6444-4-4-44-444-4-4400000000−2i2−2i22i22i22i22i2−2i2−2i200000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ6544-4-4-44-44-444-4000000002i22i2−2i2−2i2−2i2−2i22i22i200000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ6644-4-4-44-44-444-400000000−2i2−2i22i22i22i22i2−2i2−2i2000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ674-44-44-4-4400000004i−4i−4i4i02i2−2i2−2i22i22i2−2i2−2i22i20000000000000000−222222−2200000000000000000000000000000000
χ684-44-44-4-4400000004i−4i−4i4i0−2i22i22i2−2i2−2i22i22i2−2i2000000000000000022−22−222200000000000000000000000000000000
χ694-44-44-4-440000000−4i4i4i−4i02i2−2i2−2i22i22i2−2i2−2i22i2000000000000000022−22−222200000000000000000000000000000000
χ704-44-44-4-440000000−4i4i4i−4i0−2i22i22i2−2i2−2i22i22i2−2i20000000000000000−222222−2200000000000000000000000000000000
χ714-44-4-444-40000000000002i2−2i2−2i22i2−2i22i22i2−2i200004i−4i00000022−2222−22000000000000000000000000000000000000
χ724-44-4-444-40000000000002i2−2i2−2i22i2−2i22i22i2−2i20000−4i4i000000−2222−2222000000000000000000000000000000000000
χ734-44-4-444-4000000000000−2i22i22i2−2i22i2−2i2−2i22i200004i−4i000000−2222−2222000000000000000000000000000000000000
χ744-44-4-444-4000000000000−2i22i22i2−2i22i2−2i2−2i22i20000−4i4i00000022−2222−22000000000000000000000000000000000000
χ754-4-4444-4-400004-4-44i−4i4i−4i400000000000000−4i4i00000000000000000000000000000000000000000000
χ764-4-4444-4-400004-4-4−4i4i−4i4i4000000000000004i−4i00000000000000000000000000000000000000000000
χ774-4-44-4-44400004-440000-4000000000000000000004i−4i−4i4i000000000000000000000000000000000000
χ784-4-44-4-44400004-440000-400000000000000000000−4i4i4i−4i000000000000000000000000000000000000
χ794-4-44-4-4440000-44-4000044-44-4-44-440000000000000000000000000000000000000000000000000000
χ804-4-44-4-4440000-44-400004-44-444-44-40000000000000000000000000000000000000000000000000000

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