Finite Group Databasebeta

← Group #100310

Character table — Group #100310

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222444444444444444444444444448888888822444888888888888888888888888888844
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
χ51111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ61111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ81111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ911111111111-1-1-1-1-1-11-1-1-1-1-1111111-1-1-1-1-1iiii−i−i−i−i111-1-1ii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−i11-1-11-1
χ1011111111111-1-1-1-1-1-11-1-1-1-1-1111111-1-1-1-1-1iiii−i−i−i−i111-1-1ii−i−iiiii−i−i−i−i−i−i−i−iiiii−i−iii-1-111-11
χ1111111111111-1-1-1-1-1-11-1-1-1-1-1111111-1-1-1-1-1−i−i−i−iiiii111-1-1−i−iii−i−i−i−iiiiiiiii−i−i−i−iii−i−i-1-111-11
χ1211111111111-1-1-1-1-1-11-1-1-1-1-1111111-1-1-1-1-1−i−i−i−iiiii111-1-1−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii11-1-11-1
χ1311111111111-1-1-1-1-1-11-1-1-1-1-111-1-1-1-11111-1iiii−i−i−i−i-1-1111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii11-1-1-11
χ1411111111111-1-1-1-1-1-11-1-1-1-1-111-1-1-1-11111-1iiii−i−i−i−i-1-1111ii−i−i−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-1111-1
χ1511111111111-1-1-1-1-1-11-1-1-1-1-111-1-1-1-11111-1−i−i−i−iiiii-1-1111−i−iiiiiii−i−i−i−iiiii−i−i−i−i−i−iii-1-1111-1
χ1611111111111-1-1-1-1-1-11-1-1-1-1-111-1-1-1-11111-1−i−i−i−iiiii-1-1111−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−i11-1-1-11
χ1722222222222222-2-2-222-22-2-2-2-22222-2-2-2-2200000000-2-2-222000000000000000000000000000000
χ1822222222222222-2-2-222-22-2-2-2-2-2-2-2-2222220000000022-2-2-2000000000000000000000000000000
χ1922222222222-2-2-22222-22-222-2-222222222-200000000-2-2-2-2-2000000000000000000000000000000
χ2022222222222-2-2-22222-22-222-2-2-2-2-2-2-2-2-2-2-20000000022-222000000000000000000000000000000
χ2122222222-2-2-2222222-222-2-2-22200000000-22222222200-200-2-2-2-200000000000000000000000000
χ2222222222-2-2-2222222-222-2-2-22200000000-2-2-2-2-2-2-2-2-200-200222200000000000000000000000000
χ2322222222-2-2-2222-2-2-2-22-2-222-2-200000000-2000000000020000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ2422222222-2-2-2222-2-2-2-22-2-222-2-200000000-200000000002000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ2522222222-2-2-2-2-2-2222-2-222-2-2-2-20000000020000000000200000022-2-2-2-222000000000000000000
χ2622222222-2-2-2-2-2-2222-2-222-2-2-2-200000000200000000002000000-2-22222-2-2000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222220000000022i2i2i2i−2i−2i−2i−2i00-200−2i−2i2i2i00000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222000000002−2i−2i−2i−2i2i2i2i2i00-2002i2i−2i−2i00000000000000000000000000
χ29222-2-22-2-222-222-2000-2-2020000000022-2-2-222−2−222−2−22-20002−22−22−22−22−22−2000000000000000000
χ30222-2-22-2-222-222-2000-2-2020000000022-2-2-2−2−222−2−2222-2000−22−22−22−22−22−22000000000000000000
χ31222-2-22-2-222-222-2000-2-20200000000-2-222-222−2−222−2−2-220002−22−2−22−22−22−22000000000000000000
χ32222-2-22-2-222-222-2000-2-20200000000-2-222-2−2−222−2−222-22000−22−222−22−22−22−2000000000000000000
χ33222-2-22-2-222-2-2-22000-220-20000000022-2-22i2i2−i2−i2−i2−i2i2i2-22000i2−i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000000000
χ34222-2-22-2-222-2-2-22000-220-20000000022-2-22−i2−i2i2i2i2i2−i2−i2-22000−i2i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000000000
χ35222-2-22-2-222-2-2-22000-220-200000000-2-2222i2i2−i2−i2−i2−i2i2i22-2000i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000000000
χ36222-2-22-2-222-2-2-22000-220-200000000-2-2222−i2−i2i2i2i2i2−i2−i22-2000−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000000000
χ37222-2-22-2-2-2-2222-20002-20-200002i2i−2i−2i0000222−2−222−2−20002i−2i−22−22i2−i2−i2i2i2−i2−i2i2000000000000000000
χ38222-2-22-2-2-2-2222-20002-20-200002i2i−2i−2i00002−2−222−2−2220002i−2i2−22−2−i2i2i2−i2−i2i2i2−i2000000000000000000
χ39222-2-22-2-2-2-2222-20002-20-20000−2i−2i2i2i0000222−2−222−2−2000−2i2i−22−22−i2i2i2−i2−i2i2i2−i2000000000000000000
χ40222-2-22-2-2-2-2222-20002-20-20000−2i−2i2i2i00002−2−222−2−222000−2i2i2−22−2i2−i2−i2i2i2−i2−i2i2000000000000000000
χ41222-2-22-2-2-2-22-2-22000220200002i2i−2i−2i0000-2i2i2−i2−i2−i2−i2i2i2000−2i2i−i2i2i2−i2−222−22−2−22000000000000000000
χ42222-2-22-2-2-2-22-2-22000220200002i2i−2i−2i0000-2−i2−i2i2i2i2i2−i2−i2000−2i2ii2−i2−i2i22−2−22−222−2000000000000000000
χ43222-2-22-2-2-2-22-2-2200022020000−2i−2i2i2i0000-2i2i2−i2−i2−i2−i2i2i20002i−2i−i2i2i2−i22−2−22−222−2000000000000000000
χ44222-2-22-2-2-2-22-2-2200022020000−2i−2i2i2i0000-2−i2−i2i2i2i2i2−i2−i20002i−2ii2−i2−i2i2−222−22−2−22000000000000000000
χ4522-22-2-2-222-220002-2-2-20202-2002i−2i2i−2i2i−2i2i−2i0000000000000000000000000022−2−222−2−2i2−i2i2−i2000000
χ4622-22-2-2-222-220002-2-2-20202-2002i−2i2i−2i2i−2i2i−2i00000000000000000000000000−2−222−2−222−i2i2−i2i2000000
χ4722-22-2-2-222-220002-2-2-20202-200−2i2i−2i2i−2i2i−2i2i0000000000000000000000000022−2−222−2−2−i2i2−i2i2000000
χ4822-22-2-2-222-220002-2-2-20202-200−2i2i−2i2i−2i2i−2i2i00000000000000000000000000−2−222−2−222i2−i2i2−i2000000
χ4922-22-2-2-222-22000-222-20-20-22002i−2i2i−2i−2i2i−2i2i00000000000000000000000000i2i2−i2−i2−i2−i2i2i2−222−2000000
χ5022-22-2-2-222-22000-222-20-20-22002i−2i2i−2i−2i2i−2i2i00000000000000000000000000−i2−i2i2i2i2i2−i2−i22−2−22000000
χ5122-22-2-2-222-22000-222-20-20-2200−2i2i−2i2i2i−2i2i−2i00000000000000000000000000i2i2−i2−i2−i2−i2i2i22−2−22000000
χ5222-22-2-2-222-22000-222-20-20-2200−2i2i−2i2i2i−2i2i−2i00000000000000000000000000−i2−i2i2i2i2i2−i2−i2−222−2000000
χ532-2-2-2-22220002-2222-20-2-20002-20000000002i−2i2i−2i2i−2i2i−2i00000000000000000i2−i2i2−i2i2−i2i2−i200002−22−200
χ542-2-2-2-22220002-2222-20-2-20002-20000000002i−2i2i−2i2i−2i2i−2i00000000000000000−i2i2−i2i2−i2i2−i2i20000−22−2200
χ552-2-2-2-22220002-2222-20-2-20002-2000000000−2i2i−2i2i−2i2i−2i2i00000000000000000i2−i2i2−i2i2−i2i2−i20000−22−2200
χ562-2-2-2-22220002-2222-20-2-20002-2000000000−2i2i−2i2i−2i2i−2i2i00000000000000000−i2i2−i2i2−i2i2−i2i200002−22−200
χ572-2-2-2-2222000-22-2-2-220220002-20000000002-22-2-22-22000000000000000002−22−2−22−2200002−2−2200
χ582-2-2-2-2222000-22-2-2-220220002-20000000002-22-2-22-2200000000000000000−22−222−22−20000−222−200
χ592-2-2-2-2222000-22-2-2-220220002-2000000000-22-222-22-2000000000000000002−22−2−22−220000−222−200
χ602-2-2-2-2222000-22-2-2-220220002-2000000000-22-222-22-200000000000000000−22−222−22−200002−2−2200
χ6144-44-4-4-44-44-40004-4-44040-44000000000000000000000000000000000000000000000000000000
χ6244-44-4-4-44-44-4000-44440-404-4000000000000000000000000000000000000000000000000000000
χ6344-4-44-44-44-4-40000004000000000004i−4i−4i4i00000000000000000000000000000000000000000000
χ6444-4-44-44-44-4-4000000400000000000−4i4i4i−4i00000000000000000000000000000000000000000000
χ6544-4-44-44-4-444000000-400000004-4-44000000000000000000000000000000000000000000000000
χ6644-4-44-44-4-444000000-40000000-444-4000000000000000000000000000000000000000000000000
χ674-44-44-4-440000004-4400-40000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000
χ684-44-44-4-440000004-4400-4000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000
χ694-44-44-4-44000000-44-40040000000000000000000000000000000000000002-2-22-222-20000000000
χ704-44-44-4-44000000-44-4004000000000000000000000000000000000000000-222-22-2-220000000000
χ714-4-4444-4-40004-4-4000040000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000
χ724-4-4444-4-40004-4-400004000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000
χ734-4-4444-4-4000-4440000-400000000000000022−22−2222−222222−2200000000000000000000000000000000000
χ744-4-4444-4-4000-4440000-4000000000000000−222222−2222−22−222200000000000000000000000000000000000
χ754-4-4-4-44440004-44-4-440-44000-440000000000000000000000000000000000000000000000000000
χ764-4-4-4-4444000-44-444-404-4000-440000000000000000000000000000000000000000000000000000
χ778-888-8-88-8000000000000000000000000000000000000000000000000000000000000000000000

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