Finite Group Databasebeta

← Group #10801113

Character table — Group #10801113

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222222222444444444444444444666666668888888888888888888888881212121212121212121212121616161616162424242424242424
order122222344446662244444444446612121212444444444444668888121212121212121212121212121222222244444412122424242444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-111-1-1-1-1-1-11111111111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111-1-1
χ61111111111111111-1-111-1-1-1-1-1-111111111111111-1-11111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111
χ71111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-111-1-111
χ81111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-11111-1-111-1-1
χ911111111111111-1-111-1-111-1-1-1-11111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111
χ1011111111111111-1-111-1-111-1-1-1-111111111111111-1-111-1-111-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1
χ1111111111111111-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11111-1-1
χ1211111111111111-1-111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-11111-1-111111111-1-1-1-111-1-111-1-1-1-111
χ1311111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ1411111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1511111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ1611111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-111111111-1-1-1-1
χ171-11-11-111-11-1-11-11-1i−i1-1i−iii−i−i-111-11-1ii−i−iii−i−ii−i1-11-1i−i1-1i−i1-1i−iii−i−i11-1-11-111-1-1i−ii−i1-1i−ii−i1-11-1i−i1-1i−i
χ181-11-11-111-11-1-11-11-1i−i1-1i−iii−i−i-111-11-1ii−i−iii−i−i−ii-111-1−ii-11i−i1-1i−iii−i−i-1-1111-111-1-1i−ii−i1-1−ii−ii-11-11−ii-11−ii
χ191-11-11-111-11-1-11-11-1i−i1-1i−iii−i−i-111-11-1−i−iii−i−iiii−i1-11-1i−i1-1i−i1-1i−iii−i−i11-1-1-11-1-111−ii−ii-11i−ii−i1-1-11−ii-11−ii
χ201-11-11-111-11-1-11-11-1i−i1-1i−iii−i−i-111-11-1−i−iii−i−iii−ii-111-1−ii-11i−i1-1i−iii−i−i-1-111-11-1-111−ii−ii-11−ii−ii-111-1i−i1-1i−i
χ211-11-11-111-11-1-11-11-1−ii1-1−ii−i−iii-111-11-1ii−i−iii−i−ii−i-111-1i−i-11−ii1-1−ii−i−iii-1-111-11-1-111i−ii−i-11i−ii−i-111-1−ii1-1−ii
χ221-11-11-111-11-1-11-11-1−ii1-1−ii−i−iii-111-11-1ii−i−iii−i−i−ii1-11-1−ii1-1−ii1-1−ii−i−iii11-1-1-11-1-111i−ii−i-11−ii−ii1-1-11i−i-11i−i
χ231-11-11-111-11-1-11-11-1−ii1-1−ii−i−iii-111-11-1−i−iii−i−iiii−i-111-1i−i-11−ii1-1−ii−i−iii-1-1111-111-1-1−ii−ii1-1i−ii−i-11-11i−i-11i−i
χ241-11-11-111-11-1-11-11-1−ii1-1−ii−i−iii-111-11-1−i−iii−i−iii−ii1-11-1−ii1-1−ii1-1−ii−i−iii11-1-11-111-1-1−ii−ii1-1−ii−ii1-11-1−ii1-1−ii
χ251-11-11-111-11-1-11-1-11i−i-11i−i−i−iii-111-11-1ii−i−iii−i−ii−i-11-11−ii1-1i−i-11i−i−i−iii-1-1111-1-1-111−ii−ii1-1i−i−ii1-11-1−ii-11i−i
χ261-11-11-111-11-1-11-1-11i−i-11i−i−i−iii-111-11-1ii−i−iii−i−i−ii1-1-11i−i-11i−i-11i−i−i−iii11-1-11-1-1-111−ii−ii1-1−iii−i-11-11i−i1-1−ii
χ271-11-11-111-11-1-11-1-11i−i-11i−i−i−iii-111-11-1−i−iii−i−iiii−i-11-11−ii1-1i−i-11i−i−i−iii-1-111-1111-1-1i−ii−i-11i−i−ii1-1-11i−i1-1−ii
χ281-11-11-111-11-1-11-1-11i−i-11i−i−i−iii-111-11-1−i−iii−i−iii−ii1-1-11i−i-11i−i-11i−i−i−iii11-1-1-1111-1-1i−ii−i-11−iii−i-111-1−ii-11i−i
χ291-11-11-111-11-1-11-1-11−ii-11−iiii−i−i-111-11-1ii−i−iii−i−ii−i1-1-11−ii-11−ii-11−iiii−i−i11-1-1-1111-1-1−ii−ii-11i−i−ii-111-1i−i-11−ii
χ301-11-11-111-11-1-11-1-11−ii-11−iiii−i−i-111-11-1ii−i−iii−i−i−ii-11-11i−i1-1−ii-11−iiii−i−i-1-111-1111-1-1−ii−ii-11−iii−i1-1-11−ii1-1i−i
χ311-11-11-111-11-1-11-1-11−ii-11−iiii−i−i-111-11-1−i−iii−i−iiii−i1-1-11−ii-11−ii-11−iiii−i−i11-1-11-1-1-111i−ii−i1-1i−i−ii-11-11−ii1-1i−i
χ321-11-11-111-11-1-11-1-11−ii-11−iiii−i−i-111-11-1−i−iii−i−iii−ii-11-11i−i1-1−ii-11−iiii−i−i-1-1111-1-1-111i−ii−i1-1−iii−i1-11-1i−i-11−ii
χ332222222-2-2-2-2222000000002-22-222-2-2-2-22222-2-2-2-200000000000000002-22-20000002-22-200000000000000000000
χ342222222-2-2-2-2222000000002-22-222-2-2-2-2-2-2-2-2222200000000000000002-22-2000000-22-2200000000000000000000
χ352222222-2-2-2-222200000000-22-2222-2-2-2-22222-2-2-2-20000000000000000-22-22000000-22-2200000000000000000000
χ362222222-2-2-2-222200000000-22-2222-2-2-2-2-2-2-2-222220000000000000000-22-220000002-22-200000000000000000000
χ37222222-12222-1-1-1222222222222-1-1-1-1-1-1000000002222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1-1-100000000
χ38222222-12222-1-1-1222222222222-1-1-1-1-1-100000000-2-2-2-2-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111100000000000011111100000000
χ39222222-12222-1-1-122-2-222-2-2-2-2-2-2-1-1-1-1-1-10000000022-2-2-1-122-2-211-1-11111111111000000000000-1-1-1-11100000000
χ40222222-12222-1-1-122-2-222-2-2-2-2-2-2-1-1-1-1-1-100000000-2-222-1-1-2-22211-1-1111111-1-1-1-10000000000001111-1-100000000
χ41222222-12222-1-1-1-2-222-2-222-2-2-2-2-1-1-1-1-1-10000000022-2-211-2-222-1-111-1-111111111000000000000-1-111-1-100000000
χ42222222-12222-1-1-1-2-222-2-222-2-2-2-2-1-1-1-1-1-100000000-2-2221122-2-2-1-111-1-11111-1-1-1-100000000000011-1-11100000000
χ43222222-12222-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-100000000222211-2-2-2-2111111-1-1-1-1-1-1-1-1000000000000-1-1111100000000
χ44222222-12222-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-100000000-2-2-2-2112222111111-1-1-1-1111100000000000011-1-1-1-100000000
χ452222-2-222-2-22222002200-2-20000-2-2-222-22-22-22-22-200000000002200-2-2000000002200000000-2-200000000000000
χ462222-2-222-2-22222002200-2-20000-2-2-222-2-22-22-22-2200000000002200-2-200000000-2-2000000002200000000000000
χ472222-2-222-2-2222200-2-200220000-2-2-222-22-22-22-22-20000000000-2-2002200000000-2-2000000002200000000000000
χ482222-2-222-2-2222200-2-200220000-2-2-222-2-22-22-22-220000000000-2-20022000000002200000000-2-200000000000000
χ492222-2-22-222-22222200-2-2000000-2-22-2-222-22-2-22-22000022000000-2-20000000000000000-2-2220000000000000000
χ502222-2-22-222-22222200-2-2000000-2-22-2-22-22-222-22-2000022000000-2-2000000000000000022-2-20000000000000000
χ512222-2-22-222-2222-2-20022000000-2-22-2-222-22-2-22-220000-2-200000022000000000000000022-2-20000000000000000
χ522222-2-22-222-2222-2-20022000000-2-22-2-22-22-222-22-20000-2-2000000220000000000000000-2-2220000000000000000
χ532-22-22-22-22-22-22-2000000002i−2i−2i2i-22-22-222i2i−2i−2i−2i−2i2i2i00000000000000002i−2i−2i2i0000002-2-2200000000000000000000
χ542-22-22-22-22-22-22-2000000002i−2i−2i2i-22-22-22−2i−2i2i2i2i2i−2i−2i00000000000000002i−2i−2i2i000000-222-200000000000000000000
χ552-22-22-22-22-22-22-200000000−2i2i2i−2i-22-22-222i2i−2i−2i−2i−2i2i2i0000000000000000−2i2i2i−2i000000-222-200000000000000000000
χ562-22-22-22-22-22-22-200000000−2i2i2i−2i-22-22-22−2i−2i2i2i2i2i−2i−2i0000000000000000−2i2i2i−2i0000002-2-2200000000000000000000
χ572-22-22-2-12-22-21-112-22i−2i2-22i−2i2i2i−2i−2i1-1-11-11000000002i−2i2-2-112i−2i2-2−ii-11−ii−i−iii-1-111000000000000−ii−ii-1100000000
χ582-22-22-2-12-22-21-112-22i−2i2-22i−2i2i2i−2i−2i1-1-11-1100000000−2i2i-22-11−2i2i-22−ii-11−ii−i−iii11-1-1000000000000i−ii−i1-100000000
χ592-22-22-2-12-22-21-112-2−2i2i2-2−2i2i−2i−2i2i2i1-1-11-11000000002i−2i-22-112i−2i-22i−i-11i−iii−i−i11-1-1000000000000−ii−ii1-100000000
χ602-22-22-2-12-22-21-112-2−2i2i2-2−2i2i−2i−2i2i2i1-1-11-1100000000−2i2i2-2-11−2i2i2-2i−i-11i−iii−i−i-1-111000000000000i−ii−i-1100000000
χ612-22-22-2-12-22-21-11-222i−2i-222i−2i−2i−2i2i2i1-1-11-11000000002i−2i-221-1−2i2i2-2−ii1-1−iiii−i−i11-1-1000000000000−iii−i-1100000000
χ622-22-22-2-12-22-21-11-222i−2i-222i−2i−2i−2i2i2i1-1-11-1100000000−2i2i2-21-12i−2i-22−ii1-1−iiii−i−i-1-111000000000000i−i−ii1-100000000
χ632-22-22-2-12-22-21-11-22−2i2i-22−2i2i2i2i−2i−2i1-1-11-11000000002i−2i2-21-1−2i2i-22i−i1-1i−i−i−iii-1-111000000000000−iii−i1-100000000
χ642-22-22-2-12-22-21-11-22−2i2i-22−2i2i2i2i−2i−2i1-1-11-1100000000−2i2i-221-12i−2i2-2i−i1-1i−i−i−iii11-1-1000000000000i−i−ii-1100000000
χ652-22-2-22222-2-2-22-2002i−2i00−2i2i00002-2-2-2222i−2i−2i2i2i−2i−2i2i00000000002i−2i00−2i2i000000002-200000000-2200000000000000
χ662-22-2-22222-2-2-22-2002i−2i00−2i2i00002-2-2-222−2i2i2i−2i−2i2i2i−2i00000000002i−2i00−2i2i00000000-22000000002-200000000000000
χ672-22-2-22222-2-2-22-200−2i2i002i−2i00002-2-2-2222i−2i−2i2i2i−2i−2i2i0000000000−2i2i002i−2i00000000-22000000002-200000000000000
χ682-22-2-22222-2-2-22-200−2i2i002i−2i00002-2-2-222−2i2i2i−2i−2i2i2i−2i0000000000−2i2i002i−2i000000002-200000000-2200000000000000
χ692-22-2-222-2-222-22-22-200-220000002-222-2-22i−2i−2i2i−2i2i2i−2i00002-2000000-220000000000000000−2i2i2i−2i0000000000000000
χ702-22-2-222-2-222-22-22-200-220000002-222-2-2−2i2i2i−2i2i−2i−2i2i00002-2000000-2200000000000000002i−2i−2i2i0000000000000000
χ712-22-2-222-2-222-22-2-22002-20000002-222-2-22i−2i−2i2i−2i2i2i−2i0000-220000002-200000000000000002i−2i−2i2i0000000000000000
χ722-22-2-222-2-222-22-2-22002-20000002-222-2-2−2i2i2i−2i2i−2i−2i2i0000-220000002-20000000000000000−2i2i2i−2i0000000000000000
χ73444444-2-4-4-4-4-2-2-2000000004-44-4-2-22222000000000000000000000000-22-22000000000000000000000000000000
χ74444444-2-4-4-4-4-2-2-200000000-44-44-2-222220000000000000000000000002-22-2000000000000000000000000000000
χ754444-4-4-24-4-44-2-2-2004400-4-40000222-2-22000000000000000000-2-200220000000000000000000000000000000000
χ764444-4-4-24-4-44-2-2-200-4-400440000222-2-220000000000000000002200-2-20000000000000000000000000000000000
χ774444-4-4-2-444-4-2-2-24400-4-400000022-222-2000000000000-2-200000022000000000000000000000000000000000000
χ784444-4-4-2-444-4-2-2-2-4-4004400000022-222-200000000000022000000-2-2000000000000000000000000000000000000
χ794-44-44-4-2-44-442-22000000004i−4i−4i4i2-22-22-2000000000000000000000000−2i2i2i−2i000000000000000000000000000000
χ804-44-44-4-2-44-442-2200000000−4i4i4i−4i2-22-22-20000000000000000000000002i−2i−2i2i000000000000000000000000000000
χ814-44-4-44-244-4-42-22004i−4i00−4i4i0000-2222-2-2000000000000000000−2i2i002i−2i0000000000000000000000000000000000
χ824-44-4-44-244-4-42-2200−4i4i004i−4i0000-2222-2-20000000000000000002i−2i00−2i2i0000000000000000000000000000000000
χ834-44-4-44-2-4-4442-224-400-44000000-22-2-222000000000000-220000002-2000000000000000000000000000000000000
χ844-44-4-44-2-4-4442-22-44004-4000000-22-2-2220000000000002-2000000-22000000000000000000000000000000000000
χ8588-8-800800008-8-80000000000000000000000000000000000000000000000000000000000000000000000000000
χ8688-8-800-40000-4440000000000000000000000000000000000000000000000−2i32i3−2i32i300000000000000000000000000
χ8788-8-800-40000-44400000000000000000000000000000000000000000000002i3−2i32i3−2i300000000000000000000000000
χ888-8-880080000-8-880000000000000000000000000000000000000000000000000000000000000000000000000000
χ898-8-8800-4000044-40000000000000000000000000000000000000000000000−2i32i32i3−2i300000000000000000000000000
χ908-8-8800-4000044-400000000000000000000000000000000000000000000002i3−2i3−2i32i300000000000000000000000000

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