Finite Group Databasebeta

← Group #98930

Character table — Group #98930

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222222244444444888888884444444488888888888822444444888888884444444488888888
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
χ911111111-1-1-1-1-1-1111-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111ii−i−iii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1111-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111−i−iii−i−iii−i−iii−i−iii
χ1111111111-1-1-1-1-1-1111-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1ii−i−iii−i−i−i−iii−i−iii
χ1211111111-1-1-1-1-1-1111-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1−i−iii−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-1-1-1111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1ii−i−i−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-1-1-1111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1−i−iiiii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111ii−i−i−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222-2-2-222-20000000022-2-2-2-2-2-20000000000002222-2-2-2-2000000000000000000000000
χ1822222222222222-2-2-222-20000000022-2-2-2-2-2-2000000000000-2-2-2-22222000000000000000000000000
χ19222222222222-2-2222-2-2222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ20222222222222-2-2222-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-200000000000000000000000000000000
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
χ2322222222-2-2-2-22222222222222222-2-2-2-222-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2422222222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-22222-2-2-2-2222200000000000000000000000000000000
χ2522222222-2-2-2-222-2-2-222-200000000-2-222-2-222000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2622222222-2-2-2-222-2-2-222-200000000-2-222-2-22200000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-2222200000000000022-2-222-2-2000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-22222000000000000-2-222-2-222000000000000000000000000
χ29222-2-2-2-2200002i−2i-2222i−2i-22i2i2i2i−2i−2i−2i−2i00002i−2i00000022-2-2000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ30222-2-2-2-2200002i−2i-2222i−2i-22i2i2i2i−2i−2i−2i−2i00002i−2i00000022-2-200000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ31222-2-2-2-2200002i−2i-2222i−2i-2−2i−2i−2i−2i2i2i2i2i00002i−2i000000-2-222000000000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i00000000
χ32222-2-2-2-2200002i−2i-2222i−2i-2−2i−2i−2i−2i2i2i2i2i00002i−2i000000-2-22200000000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i00000000
χ33222-2-2-2-220000−2i2i-222−2i2i-22i2i2i2i−2i−2i−2i−2i0000−2i2i000000-2-222000000000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i00000000
χ34222-2-2-2-220000−2i2i-222−2i2i-22i2i2i2i−2i−2i−2i−2i0000−2i2i000000-2-22200000000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i00000000
χ35222-2-2-2-220000−2i2i-222−2i2i-2−2i−2i−2i−2i2i2i2i2i0000−2i2i00000022-2-2000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ36222-2-2-2-220000−2i2i-222−2i2i-2−2i−2i−2i−2i2i2i2i2i0000−2i2i00000022-2-200000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ3722-222-2-2-222-2-222000-2-2022−2−222−2−22-200000022−2−22−22−222−2−22-22-200002−22−22−22−20000000000000000
χ3822-222-2-2-222-2-222000-2-2022−2−222−2−22-200000022−2−22−22−222−2−2-22-220000−22−22−22−220000000000000000
χ3922-222-2-2-222-2-222000-2-20−2−222−2−2222-2000000−2−222−22−22−2−2222-22-20000−22−22−22−220000000000000000
χ4022-222-2-2-222-2-222000-2-20−2−222−2−2222-2000000−2−222−22−22−2−222-22-2200002−22−22−22−20000000000000000
χ4122-222-2-2-222-2-2-2-200022022−2−222−2−2-22000000−2−222−22−2222−2−200002i−2i2i−2ii2−i2−i2i2i2−i2−i2i20000000000000000
χ4222-222-2-2-222-2-2-2-200022022−2−222−2−2-22000000−2−222−22−2222−2−20000−2i2i−2i2i−i2i2i2−i2−i2i2i2−i20000000000000000
χ4322-222-2-2-222-2-2-2-2000220−2−222−2−222-2200000022−2−22−22−2−2−22200002i−2i2i−2i−i2i2i2−i2−i2i2i2−i20000000000000000
χ4422-222-2-2-222-2-2-2-2000220−2−222−2−222-2200000022−2−22−22−2−2−2220000−2i2i−2i2ii2−i2−i2i2i2−i2−i2i20000000000000000
χ4522-222-2-2-2-2-22222000-2-2022−2−222−2−2-22000000−2−2222−22−2−2−22200002i−2i−2i2ii2−i2−i2i2−i2i2i2−i20000000000000000
χ4622-222-2-2-2-2-22222000-2-2022−2−222−2−2-22000000−2−2222−22−2−2−2220000−2i2i2i−2i−i2i2i2−i2i2−i2−i2i20000000000000000
χ4722-222-2-2-2-2-22222000-2-20−2−222−2−222-2200000022−2−2−22−2222−2−200002i−2i−2i2i−i2i2i2−i2i2−i2−i2i20000000000000000
χ4822-222-2-2-2-2-22222000-2-20−2−222−2−222-2200000022−2−2−22−2222−2−20000−2i2i2i−2ii2−i2−i2i2−i2i2i2−i20000000000000000
χ4922-222-2-2-2-2-222-2-200022022−2−222−2−22-200000022−2−2−22−22−2−2222-2-220000−22−222−22−20000000000000000
χ5022-222-2-2-2-2-222-2-200022022−2−222−2−22-200000022−2−2−22−22−2−222-222-200002−22−2−22−220000000000000000
χ5122-222-2-2-2-2-222-2-2000220−2−222−2−2222-2000000−2−2222−22−222−2−22-2-2200002−22−2−22−220000000000000000
χ5222-222-2-2-2-2-222-2-2000220−2−222−2−2222-2000000−2−2222−22−222−2−2-222-20000−22−222−22−20000000000000000
χ532-2-22-22-222-22-20022-200-22i−2i2i−2i2i−2i2i−2i0000002-2000000002i−2i2i−2i0000000000000000000000002−22−2i2−i2i2−i2
χ542-2-22-22-222-22-20022-200-22i−2i2i−2i2i−2i2i−2i0000002-2000000002i−2i2i−2i000000000000000000000000−22−22−i2i2−i2i2
χ552-2-22-22-222-22-20022-200-2−2i2i−2i2i−2i2i−2i2i0000002-200000000−2i2i−2i2i0000000000000000000000002−22−2−i2i2−i2i2
χ562-2-22-22-222-22-20022-200-2−2i2i−2i2i−2i2i−2i2i0000002-200000000−2i2i−2i2i000000000000000000000000−22−22i2−i2i2−i2
χ572-2-22-22-22-22-220022-200-22i−2i2i−2i2i−2i2i−2i000000-2200000000−2i2i−2i2i000000000000000000000000i2−i2−i2i2−222−2
χ582-2-22-22-22-22-220022-200-22i−2i2i−2i2i−2i2i−2i000000-2200000000−2i2i−2i2i000000000000000000000000−i2i2i2−i22−2−22
χ592-2-22-22-22-22-220022-200-2−2i2i−2i2i−2i2i−2i2i000000-22000000002i−2i2i−2i000000000000000000000000i2−i2−i2i22−2−22
χ602-2-22-22-22-22-220022-200-2−2i2i−2i2i−2i2i−2i2i000000-22000000002i−2i2i−2i000000000000000000000000−i2i2i2−i2−222−2
χ61444-4-4-4-4400004i−4i4-4-44i−4i4000000000000−4i4i0000000000000000000000000000000000000000000000
χ62444-4-4-4-440000−4i4i4-4-4−4i4i40000000000004i−4i0000000000000000000000000000000000000000000000
χ6344-4-4-444-400004i−4i000−4i4i02i22i2−2i2−2i2−2i2−2i22i22i200000000000022−22−2222000000000000000000000000000000000000
χ6444-4-4-444-400004i−4i000−4i4i0−2i2−2i22i22i22i22i2−2i2−2i2000000000000−222222−22000000000000000000000000000000000000
χ6544-4-4-444-40000−4i4i0004i−4i02i22i2−2i2−2i2−2i2−2i22i22i2000000000000−222222−22000000000000000000000000000000000000
χ6644-4-4-444-40000−4i4i0004i−4i0−2i2−2i22i22i22i22i2−2i2−2i200000000000022−22−2222000000000000000000000000000000000000
χ674-444-4-44-44-4-44000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000002i2−2i2−2i22i200000000000000000000000000000000
χ684-444-4-44-44-4-4400000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000−2i22i22i2−2i200000000000000000000000000000000
χ694-444-4-44-4-444-4000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000−2i22i22i2−2i200000000000000000000000000000000
χ704-444-4-44-4-444-400000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000002i2−2i2−2i22i200000000000000000000000000000000
χ714-44-444-4-400000000000022−22−2222−222222−22004i−4i00002i2−2i22i2−2i20000000000000000000000000000000000000000
χ724-44-444-4-400000000000022−22−2222−222222−2200−4i4i0000−2i22i2−2i22i20000000000000000000000000000000000000000
χ734-44-444-4-4000000000000−222222−2222−22−2222004i−4i0000−2i22i2−2i22i20000000000000000000000000000000000000000
χ744-44-444-4-4000000000000−222222−2222−22−222200−4i4i00002i2−2i22i2−2i20000000000000000000000000000000000000000
χ754-4-44-44-444-44-400-4-4400400000000000000-4400000000000000000000000000000000000000000000
χ764-4-44-44-44-44-4400-4-44004000000000000004-400000000000000000000000000000000000000000000
χ774-4-4-44-4440000004-4400-400000000000000004i−4i−4i4i0000000000000000000000000000000000000000
χ784-4-4-44-4440000004-4400-40000000000000000−4i4i4i−4i0000000000000000000000000000000000000000
χ794-4-4-44-444000000-44-40044-44-4-44-440000000000000000000000000000000000000000000000000000
χ804-4-4-44-444000000-44-4004-44-444-44-40000000000000000000000000000000000000000000000000000

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