Finite Group Databasebeta

← Group #10816026

Character table — Group #10816026

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222222222222244444444444444446666888888888888888888881212121212121212121212121212121212121616161616161616242424242424
order1222223444466688882244668812121212242424248888224466888888121224242424242422444444444444448866121224242424444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-111-1-111-1-111111111-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111
χ31111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ5111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ6111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-111-1-111-1-111-1-1-1-111-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1
χ7111111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ8111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ911111111111111-1-1-1-1111111-1-11111-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-111-1-1-1-111-1-1
χ1011111111111111-1-1-1-1111111-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ1111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-111-1-111-1-111
χ1211111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-111-1-11111
χ1311111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111
χ1411111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-111-1-11111-1-111-1-111
χ1511111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111111111-1-111-1-1-1-11111-1-1-1-1
χ1611111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ171-11-1-1111-11-1-11-1ii−i−i1-11-11-1i−i11-1-1ii−i−iii−i−i1-1i−i1-11-1i−ii−i1-1i−iii−i−i1-1i−ii−i1-1i−ii−i11-1-1i−i1-1i−i1-1i−i1-1i−i1-1
χ181-11-1-1111-11-1-11-1ii−i−i1-11-11-1i−i11-1-1ii−i−iii−i−i-11−ii1-1-11i−i−ii1-1i−iii−i−i-11i−i−ii-11i−i−ii11-1-1i−i-11−ii-11−ii-11−ii1-1
χ191-11-1-1111-11-1-11-1ii−i−i1-11-11-1i−i11-1-1ii−i−i−i−iii1-1i−i1-11-1i−ii−i1-1i−iii−i−i-11−ii−ii-11−ii−ii-1-111−ii1-1i−i1-1i−i-11−ii-11
χ201-11-1-1111-11-1-11-1ii−i−i1-11-11-1i−i11-1-1ii−i−i−i−iii-11−ii1-1-11i−i−ii1-1i−iii−i−i1-1−iii−i1-1−iii−i-1-111−ii-11−ii-11−ii1-1i−i-11
χ211-11-1-1111-11-1-11-1ii−i−i-11-111-1i−i11-1-1ii−i−iii−i−i1-1i−i-11-11−ii−ii-11i−i−i−iii-11−ii−ii-11−ii−ii11-1-1i−i1-1i−i-11−ii1-1i−i-11
χ221-11-1-1111-11-1-11-1ii−i−i-11-111-1i−i11-1-1ii−i−iii−i−i-11−ii-111-1−iii−i-11i−i−i−iii1-1−iii−i1-1−iii−i11-1-1i−i-11−ii1-1i−i-11−ii-11
χ231-11-1-1111-11-1-11-1ii−i−i-11-111-1i−i11-1-1ii−i−i−i−iii1-1i−i-11-11−ii−ii-11i−i−i−iii1-1i−ii−i1-1i−ii−i-1-111−ii1-1i−i-11−ii-11−ii1-1
χ241-11-1-1111-11-1-11-1ii−i−i-11-111-1i−i11-1-1ii−i−i−i−iii-11−ii-111-1−iii−i-11i−i−i−iii-11i−i−ii-11i−i−ii-1-111−ii-11−ii1-1i−i1-1i−i1-1
χ251-11-1-1111-11-1-11-1−i−iii1-11-11-1−ii11-1-1−i−iiiii−i−i1-1−ii1-11-1−ii−ii1-1−ii−i−iii-11i−ii−i-11i−ii−i-1-111i−i1-1−ii1-1−ii-11i−i-11
χ261-11-1-1111-11-1-11-1−i−iii1-11-11-1−ii11-1-1−i−iiiii−i−i-11i−i1-1-11−iii−i1-1−ii−i−iii1-1i−i−ii1-1i−i−ii-1-111i−i-11i−i-11i−i1-1−ii-11
χ271-11-1-1111-11-1-11-1−i−iii1-11-11-1−ii11-1-1−i−iii−i−iii1-1−ii1-11-1−ii−ii1-1−ii−i−iii1-1−ii−ii1-1−ii−ii11-1-1−ii1-1−ii1-1−ii1-1−ii1-1
χ281-11-1-1111-11-1-11-1−i−iii1-11-11-1−ii11-1-1−i−iii−i−iii-11i−i1-1-11−iii−i1-1−ii−i−iii-11−iii−i-11−iii−i11-1-1−ii-11i−i-11i−i-11i−i1-1
χ291-11-1-1111-11-1-11-1−i−iii-11-111-1−ii11-1-1−i−iiiii−i−i1-1−ii-11-11i−ii−i-11−iiii−i−i1-1−ii−ii1-1−ii−ii-1-111i−i1-1−ii-11i−i-11i−i1-1
χ301-11-1-1111-11-1-11-1−i−iii-11-111-1−ii11-1-1−i−iiiii−i−i-11i−i-111-1i−i−ii-11−iiii−i−i-11−iii−i-11−iii−i-1-111i−i-11i−i1-1−ii1-1−ii1-1
χ311-11-1-1111-11-1-11-1−i−iii-11-111-1−ii11-1-1−i−iii−i−iii1-1−ii-11-11i−ii−i-11−iiii−i−i-11i−ii−i-11i−ii−i11-1-1−ii1-1−ii-11i−i1-1−ii-11
χ321-11-1-1111-11-1-11-1−i−iii-11-111-1−ii11-1-1−i−iii−i−iii-11i−i-111-1i−i−ii-11−iiii−i−i1-1i−i−ii1-1i−i−ii11-1-1−ii-11i−i1-1−ii-11i−i-11
χ33222222-12222-1-1-122222222-1-122-1-1-1-1-1-1-1-100002222-1-1222222-1-1-1-1-1-1-1-1000000000000000000-1-1-1-1-1-1-1-1000000
χ34222222-12222-1-1-122222222-1-122-1-1-1-1-1-1-1-10000-2-2-2-2-1-1-2-222-2-2-1-1-1-1-1-1-1-100000000000000000011111111000000
χ35222222-12222-1-1-12222-2-2-2-2-1-122-1-1-1-1-1-1-1-10000222211-2-2-2-2-2-211-1-11111000000000000000000-1-1-1-11111000000
χ36222222-12222-1-1-12222-2-2-2-2-1-122-1-1-1-1-1-1-1-10000-2-2-2-21122-2-22211-1-111110000000000000000001111-1-1-1-1000000
χ37222222-12222-1-1-1-2-2-2-22222-1-1-2-2-1-1-1-11111000022-2-2-1-122-2-2-2-2-1-1111111000000000000000000-1-111-1-111000000
χ38222222-12222-1-1-1-2-2-2-22222-1-1-2-2-1-1-1-111110000-2-222-1-1-2-2-2-222-1-111111100000000000000000011-1-111-1-1000000
χ39222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-2-2-1-1-1-11111000022-2-211-2-222221111-1-1-1-1000000000000000000-1-11111-1-1000000
χ40222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-2-2-1-1-1-111110000-2-222112222-2-21111-1-1-1-100000000000000000011-1-1-1-111000000
χ412222-2-222-2-22222000022-2-2-2-200-222-200002222000022000000-2-200000000-2-2000022000000-2-200000000000000
χ422222-2-222-2-22222000022-2-2-2-200-222-20000-2-2-2-2000022000000-2-200000000220000-2-20000002200000000000000
χ432222-2-222-2-222220000-2-222-2-200-222-2000022220000-2-20000002200000000220000-2-2000000-2-200000000000000
χ442222-2-222-2-222220000-2-222-2-200-222-20000-2-2-2-20000-2-20000002200000000-2-20000220000002200000000000000
χ452222-2-22-222-222222220000-2-2-2-22-2-222222000000000000000000-2-20000220022-2-200-2-200000000000000000000
χ462222-2-22-222-222222220000-2-2-2-22-2-222222000000000000000000-2-20000-2-200-2-222002200000000000000000000
χ472222-2-22-222-2222-2-2-2-20000-2-2222-2-22-2-2-2-20000000000000000002200002200-2-2-2-2002200000000000000000000
χ482222-2-22-222-2222-2-2-2-20000-2-2222-2-22-2-2-2-2000000000000000000220000-2-200222200-2-200000000000000000000
χ492-22-22-2222-2-2-22-200002-2-22-2200-22-2200002i2i−2i−2i00002-2000000-2200000000−2i2i00002i−2i000000−2i2i00000000000000
χ502-22-22-2222-2-2-22-200002-2-22-2200-22-220000−2i−2i2i2i00002-2000000-22000000002i−2i0000−2i2i0000002i−2i00000000000000
χ512-22-22-2222-2-2-22-20000-222-2-2200-22-2200002i2i−2i−2i0000-220000002-2000000002i−2i0000−2i2i000000−2i2i00000000000000
χ522-22-22-2222-2-2-22-20000-222-2-2200-22-220000−2i−2i2i2i0000-220000002-200000000−2i2i00002i−2i0000002i−2i00000000000000
χ532-22-22-22-2-222-22-22i2i−2i−2i0000-22−2i2i2-22-22i2i−2i−2i000000000000000000−2i2i00002-2002i−2i-2200−2i2i00000000000000000000
χ542-22-22-22-2-222-22-22i2i−2i−2i0000-22−2i2i2-22-22i2i−2i−2i000000000000000000−2i2i0000-2200−2i2i2-2002i−2i00000000000000000000
χ552-22-22-22-2-222-22-2−2i−2i2i2i0000-222i−2i2-22-2−2i−2i2i2i0000000000000000002i−2i00002-200−2i2i-22002i−2i00000000000000000000
χ562-22-22-22-2-222-22-2−2i−2i2i2i0000-222i−2i2-22-2−2i−2i2i2i0000000000000000002i−2i0000-22002i−2i2-200−2i2i00000000000000000000
χ572-22-2-22-12-22-21-112i2i−2i−2i2-22-2-112i−2i-1-111−i−iii00002-22i−2i-112-22i−2i2i−2i-11−ii−i−iii000000000000000000-11−ii-11−ii000000
χ582-22-2-22-12-22-21-112i2i−2i−2i2-22-2-112i−2i-1-111−i−iii0000-22−2i2i-11-222i−2i−2i2i-11−ii−i−iii0000000000000000001-1i−i1-1i−i000000
χ592-22-2-22-12-22-21-112i2i−2i−2i-22-22-112i−2i-1-111−i−iii00002-22i−2i1-1-22−2i2i−2i2i1-1−iiii−i−i000000000000000000-11−ii1-1i−i000000
χ602-22-2-22-12-22-21-112i2i−2i−2i-22-22-112i−2i-1-111−i−iii0000-22−2i2i1-12-2−2i2i2i−2i1-1−iiii−i−i0000000000000000001-1i−i-11−ii000000
χ612-22-2-22-12-22-21-11−2i−2i2i2i2-22-2-11−2i2i-1-111ii−i−i00002-2−2i2i-112-2−2i2i−2i2i-11i−iii−i−i000000000000000000-11i−i-11i−i000000
χ622-22-2-22-12-22-21-11−2i−2i2i2i2-22-2-11−2i2i-1-111ii−i−i0000-222i−2i-11-22−2i2i2i−2i-11i−iii−i−i0000000000000000001-1−ii1-1−ii000000
χ632-22-2-22-12-22-21-11−2i−2i2i2i-22-22-11−2i2i-1-111ii−i−i00002-2−2i2i1-1-222i−2i2i−2i1-1i−i−i−iii000000000000000000-11i−i1-1−ii000000
χ642-22-2-22-12-22-21-11−2i−2i2i2i-22-22-11−2i2i-1-111ii−i−i0000-222i−2i1-12-22i−2i−2i2i1-1i−i−i−iii0000000000000000001-1−ii-11i−i000000
χ654444444-4-4-4-4444000000004400-4-4-4-4000000000000000000000000000000000000000000000000000000000000
χ66444444-2-4-4-4-4-2-2-200000000-2-200222200000000000000000000000023−2323−2300000000000000000000000000000000
χ67444444-2-4-4-4-4-2-2-200000000-2-2002222000000000000000000000000−2323−232300000000000000000000000000000000
χ684444-4-4-24-4-44-2-2-2000044-4-422002-2-22000000000000-2-20000002200000000000000000000000000000000000000
χ694444-4-4-24-4-44-2-2-20000-4-44422002-2-2200000000000022000000-2-200000000000000000000000000000000000000
χ704444-4-4-2-444-4-2-2-24444000022-4-4-222-2-2-2-2-200000000000000000022000000000000000000000000000000000000
χ714444-4-4-2-444-4-2-2-2-4-4-4-400002244-222-22222000000000000000000-2-2000000000000000000000000000000000000
χ7244-4-40040000-4-4422−2222−2200000000000022−2222−22−2i22i2−2i22i2000000000000000000000000000000002i−2i2i−2i0000000000000000
χ7344-4-40040000-4-4422−2222−2200000000000022−2222−222i2−2i22i2−2i200000000000000000000000000000000−2i2i−2i2i0000000000000000
χ7444-4-40040000-4-44−2222−2222000000000000−2222−2222−2i22i2−2i22i200000000000000000000000000000000−2i2i−2i2i0000000000000000
χ7544-4-40040000-4-44−2222−2222000000000000−2222−22222i2−2i22i2−2i2000000000000000000000000000000002i−2i2i−2i0000000000000000
χ764-44-44-4-244-4-42-2200004-4-442-2002-22-2000000000000-220000002-200000000000000000000000000000000000000
χ774-44-44-4-244-4-42-220000-444-42-2002-22-20000000000002-2000000-2200000000000000000000000000000000000000
χ784-44-44-4-2-4-4442-224i4i−4i−4i00002-2−4i4i-22-22−2i−2i2i2i0000000000000000002i−2i000000000000000000000000000000000000
χ794-44-44-4-2-4-4442-22−4i−4i4i4i00002-24i−4i-22-222i2i−2i−2i000000000000000000−2i2i000000000000000000000000000000000000
χ804-44-4-444-44-44-44-4000000004-400-4-444000000000000000000000000000000000000000000000000000000000000
χ814-44-4-44-2-44-442-2200000000-220022-2-2000000000000000000000000−2i32i32i3−2i300000000000000000000000000000000
χ824-44-4-44-2-44-442-2200000000-220022-2-20000000000000000000000002i3−2i3−2i32i300000000000000000000000000000000
χ834-4-4400400004-4-4−2i22i22i2−2i2000000000000−2i22i22i2−2i222−22−222200000000000000000000000000000000−2i2i2i−2i0000000000000000
χ844-4-4400400004-4-4−2i22i22i2−2i2000000000000−2i22i22i2−2i2−222222−22000000000000000000000000000000002i−2i−2i2i0000000000000000
χ854-4-4400400004-4-42i2−2i2−2i22i20000000000002i2−2i2−2i22i222−22−2222000000000000000000000000000000002i−2i−2i2i0000000000000000
χ864-4-4400400004-4-42i2−2i2−2i22i20000000000002i2−2i2−2i22i2−222222−2200000000000000000000000000000000−2i2i2i−2i0000000000000000
χ8788-8-800-4000044-442−4242−42000000000000−2222−222200000000000000000000000000000000000000000000000000000000
χ8888-8-800-4000044-4−4242−424200000000000022−2222−2200000000000000000000000000000000000000000000000000000000
χ898-8-8800-40000-444−4i24i24i2−4i20000000000002i2−2i2−2i22i200000000000000000000000000000000000000000000000000000000
χ908-8-8800-40000-4444i2−4i2−4i24i2000000000000−2i22i22i2−2i200000000000000000000000000000000000000000000000000000000

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