Finite Group Databasebeta

← Group #98955

Character table — Group #98955

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12222222444444444444888888882244444488888888888844444444888888888888888888888888
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
χ9111111111-1-1-1-1111-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ10111111111-1-1-1-1111-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ11111111111-1-1-1-1111-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ12111111111-1-1-1-1111-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ13111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222-2-222222-2-22222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1822222222222-2-222222-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
χ19222222222-2-222222-2-22222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ20222222222-2-222222-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-200000000000000000000000000000000
χ2122222222-22222-2-2-2222200000000-2-222-2-2-2-200000000000022-2-222-2-2000000000000000000000000
χ2222222222-22222-2-2-2222200000000-2-222-2-2-2-2000000000000-2-222-2-222000000000000000000000000
χ2322222222-222-2-2-2-2-222-2-200000000-2-2-2-22222000000000000000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ2422222222-222-2-2-2-2-222-2-200000000-2-2-2-2222200000000000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2522222222-2-2-222-2-2-2-2-2220000000022-2-222-2-2000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ2622222222-2-2-222-2-2-2-2-2220000000022-2-222-2-200000000000000000000−2i−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
χ292222-2-2-2-2222002-2-2-2-2002222-2-2-2-22-200000022-2-2000000000000000000000000000000002−22−22−22−2
χ302222-2-2-2-2222002-2-2-2-2002222-2-2-2-22-200000022-2-200000000000000000000000000000000−22−22−22−22
χ312222-2-2-2-2222002-2-2-2-200-2-2-2-222222-2000000-2-222000000000000000000000000000000002−22−2−22−22
χ322222-2-2-2-2222002-2-2-2-200-2-2-2-222222-2000000-2-22200000000000000000000000000000000−22−222−22−2
χ332222-2-2-2-22-2-2002-2-222002222-2-2-2-2-22000000-2-22200000000000000000000000000000000i2−i2−i2i2i2−i2−i2i2
χ342222-2-2-2-22-2-2002-2-222002222-2-2-2-2-22000000-2-22200000000000000000000000000000000−i2i2i2−i2−i2i2i2−i2
χ352222-2-2-2-22-2-2002-2-22200-2-2-2-22222-2200000022-2-200000000000000000000000000000000i2−i2−i2i2−i2i2i2−i2
χ362222-2-2-2-22-2-2002-2-22200-2-2-2-22222-2200000022-2-200000000000000000000000000000000−i2i2i2−i2i2−i2−i2i2
χ3722-2-22-22-202i−2i2i−2i0002i−2i2i−2i22−2−222−2−2002-20000i2−i2i2−i222−2−2i2i2−i2−i2002i−2i002-2i2−i2i2−i22−22−20000000000000000
χ3822-2-22-22-202i−2i2i−2i0002i−2i2i−2i22−2−222−2−2002-20000i2−i2i2−i222−2−2i2i2−i2−i200−2i2i00-22−i2i2−i2i2−22−220000000000000000
χ3922-2-22-22-202i−2i2i−2i0002i−2i2i−2i−2−222−2−222002-20000−i2i2−i2i2−2−222−i2−i2i2i2002i−2i002-2−i2i2−i2i2−22−220000000000000000
χ4022-2-22-22-202i−2i2i−2i0002i−2i2i−2i−2−222−2−222002-20000−i2i2−i2i2−2−222−i2−i2i2i200−2i2i00-22i2−i2i2−i22−22−20000000000000000
χ4122-2-22-22-202i−2i−2i2i0002i−2i−2i2i22−2−222−2−200-220000i2−i2i2−i2−2−222−i2−i2i2i22-2002i−2i002−2−22−i2i2i2−i20000000000000000
χ4222-2-22-22-202i−2i−2i2i0002i−2i−2i2i22−2−222−2−200-220000i2−i2i2−i2−2−222−i2−i2i2i2-2200−2i2i00−222−2i2−i2−i2i20000000000000000
χ4322-2-22-22-202i−2i−2i2i0002i−2i−2i2i−2−222−2−22200-220000−i2i2−i2i222−2−2i2i2−i2−i22-2002i−2i00−222−2i2−i2−i2i20000000000000000
χ4422-2-22-22-202i−2i−2i2i0002i−2i−2i2i−2−222−2−22200-220000−i2i2−i2i222−2−2i2i2−i2−i2-2200−2i2i002−2−22−i2i2i2−i20000000000000000
χ4522-2-22-22-20−2i2i2i−2i000−2i2i2i−2i22−2−222−2−200-220000−i2i2−i2i2−2−222i2i2−i2−i22-200−2i2i002−2−22i2−i2−i2i20000000000000000
χ4622-2-22-22-20−2i2i2i−2i000−2i2i2i−2i22−2−222−2−200-220000−i2i2−i2i2−2−222i2i2−i2−i2-22002i−2i00−222−2−i2i2i2−i20000000000000000
χ4722-2-22-22-20−2i2i2i−2i000−2i2i2i−2i−2−222−2−22200-220000i2−i2i2−i222−2−2−i2−i2i2i22-200−2i2i00−222−2−i2i2i2−i20000000000000000
χ4822-2-22-22-20−2i2i2i−2i000−2i2i2i−2i−2−222−2−22200-220000i2−i2i2−i222−2−2−i2−i2i2i2-22002i−2i002−2−22i2−i2−i2i20000000000000000
χ4922-2-22-22-20−2i2i−2i2i000−2i2i−2i2i22−2−222−2−2002-20000−i2i2−i2i222−2−2−i2−i2i2i2002i−2i00-22i2−i2i2−i2−22−220000000000000000
χ5022-2-22-22-20−2i2i−2i2i000−2i2i−2i2i22−2−222−2−2002-20000−i2i2−i2i222−2−2−i2−i2i2i200−2i2i002-2−i2i2−i2i22−22−20000000000000000
χ5122-2-22-22-20−2i2i−2i2i000−2i2i−2i2i−2−222−2−222002-20000i2−i2i2−i2−2−222i2i2−i2−i2002i−2i00-22−i2i2−i2i22−22−20000000000000000
χ5222-2-22-22-20−2i2i−2i2i000−2i2i−2i2i−2−222−2−222002-20000i2−i2i2−i2−2−222i2i2−i2−i200−2i2i002-2i2−i2i2−i2−22−220000000000000000
χ532-2-2222-2-2-2002i−2i22-200−2i2i2-22-22-22-20000002i−2i000000002i−2i2i−2i00000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ542-2-2222-2-2-2002i−2i22-200−2i2i2-22-22-22-20000002i−2i000000002i−2i2i−2i0000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ552-2-2222-2-2-2002i−2i22-200−2i2i-22-22-22-220000002i−2i00000000−2i2i−2i2i00000000000000001+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000
χ562-2-2222-2-2-2002i−2i22-200−2i2i-22-22-22-220000002i−2i00000000−2i2i−2i2i0000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i00000000
χ572-2-2222-2-2-200−2i2i22-2002i−2i2-22-22-22-2000000−2i2i00000000−2i2i−2i2i00000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ582-2-2222-2-2-200−2i2i22-2002i−2i2-22-22-22-2000000−2i2i00000000−2i2i−2i2i0000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ592-2-2222-2-2-200−2i2i22-2002i−2i-22-22-22-22000000−2i2i000000002i−2i2i−2i00000000000000001−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000
χ602-2-2222-2-2-200−2i2i22-2002i−2i-22-22-22-22000000−2i2i000000002i−2i2i−2i0000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000
χ614444-4-4-4-4-44400-444-4-40000000000-4400000000000000000000000000000000000000000000000000
χ624444-4-4-4-4-4-4-400-4444400000000004-400000000000000000000000000000000000000000000000000
χ6344-4-4-44-4404i−4i00000−4i4i002222−22−22−22−222222000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ6444-4-4-44-4404i−4i00000−4i4i00−22−2222222222−22−2200000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ6544-4-4-44-440−4i4i000004i−4i002222−22−22−22−22222200000000−2i22i22i2−2i20000000000000000000000000000000000000000
χ6644-4-4-44-440−4i4i000004i−4i00−22−2222222222−22−22000000002i2−2i2−2i22i20000000000000000000000000000000000000000
χ674-44-44-4-440004400000-4-422−22−222222−22−2222000000000000000022−22−222200000000000000000000000000000000
χ684-44-44-4-440004400000-4-4−222222−22−222222−220000000000000000−222222−2200000000000000000000000000000000
χ694-44-44-4-44000-4-4000004422−22−222222−22−22220000000000000000−222222−2200000000000000000000000000000000
χ704-44-44-4-44000-4-40000044−222222−22−222222−22000000000000000022−22−222200000000000000000000000000000000
χ714-44-4-444-400000000000022−22−2222−222222−2200004i−4i0000002i2−2i22i2−2i2000000000000000000000000000000000000
χ724-44-4-444-400000000000022−22−2222−222222−220000−4i4i000000−2i22i2−2i22i2000000000000000000000000000000000000
χ734-44-4-444-4000000000000−222222−2222−22−222200004i−4i000000−2i22i2−2i22i2000000000000000000000000000000000000
χ744-44-4-444-4000000000000−222222−2222−22−22220000−4i4i0000002i2−2i22i2−2i2000000000000000000000000000000000000
χ754-4-4444-4-44004i−4i-4-4400−4i4i00000000000000−4i4i00000000000000000000000000000000000000000000
χ764-4-4444-4-4400−4i4i-4-44004i−4i000000000000004i−4i00000000000000000000000000000000000000000000
χ774-4-44-4-44440000-44-40000000000000000000000004i−4i−4i4i000000000000000000000000000000000000
χ784-4-44-4-44440000-44-4000000000000000000000000−4i4i4i−4i000000000000000000000000000000000000
χ794-4-44-4-444-400004-4400004-44-4-44-440000000000000000000000000000000000000000000000000000
χ804-4-44-4-444-400004-440000-44-444-44-40000000000000000000000000000000000000000000000000000

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