Finite Group Databasebeta

← Group #11788694

Character table — Group #11788694

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size11222444444446666888888888991212121212121212121216161818182424242424242424242436364848484872727272
order1224423346612128888666612121212122288888824242424612244448824242424242424121224244488
χ1111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ511111-111-11111111111-1-11-1-1111111-1-1-1-11111-1-111111-1-111-1-1-1-1-1-111-1-111-1-1
χ611111-111-11111111111-1-11-1-1111111-1-1-1-11111-1-1111-1-11111-1-1-1-1-1-1-1-111-1-111
χ711111-111-11111-1-1-1-111-1-11-1-11111-1-11111-1-1-1-1-1-111111-1-1-1-11111-1-111-1-1-1-111
χ811111-111-11111-1-1-1-111-1-11-1-11111-1-11111-1-1-1-1-1-1111-1-111-1-11111-1-1-1-11111-1-1
χ911-11-1111-111-1-1ii−i−i-1-1111-1-1-11-1-1i−iii−i−iii−i−i1-111-11-11-1i−iii−i−i-111-11-1i−ii−i
χ1011-11-1111-111-1-1ii−i−i-1-1111-1-1-11-1-1i−iii−i−iii−i−i1-111-1-11-11i−iii−i−i-11-11-11−ii−ii
χ1111-11-1111-111-1-1−i−iii-1-1111-1-1-11-1-1−ii−i−iii−i−iii1-111-11-11-1−ii−i−iii-111-11-1−ii−ii
χ1211-11-1111-111-1-1−i−iii-1-1111-1-1-11-1-1−ii−i−iii−i−iii1-111-1-11-11−ii−i−iii-11-11-11i−ii−i
χ1311-11-1-111111-1-1ii−i−i-1-1-1-1111-11-1-1i−i−i−iiiii−i−i-1111-11-1-11i−i−i−iii1-11-1-11i−i−ii
χ1411-11-1-111111-1-1ii−i−i-1-1-1-1111-11-1-1i−i−i−iiiii−i−i-1111-1-111-1i−i−i−iii1-1-111-1−iii−i
χ1511-11-1-111111-1-1−i−iii-1-1-1-1111-11-1-1−iiii−i−i−i−iii-1111-11-1-11−iiii−i−i1-11-1-11−iii−i
χ1611-11-1-111111-1-1−i−iii-1-1-1-1111-11-1-1−iiii−i−i−i−iii-1111-1-111-1−iiii−i−i1-1-111-1i−i−ii
χ1722222222222220000222222222-2-2000000000022-2-2-20000000000-2-200000000
χ1822222-222-22222000022-2-22-2-222-2-20000000000-2-2-2-2-200000000002200000000
χ19222-2-2022022-2-200002200-200-2-222002i−2i2i−2i0000002-2-20000002i−2i2i−2i0000000000
χ20222-2-2022022-2-200002200-200-2-22200−2i2i−2i2i0000002-2-2000000−2i2i−2i2i0000000000
χ21222-2-2022022-2-22i2i−2i−2i2200-200-2-2-2-2−2i2i00002i2i−2i−2i00-2220000−2i2i00000000000000
χ22222-2-2022022-2-2−2i−2i2i2i2200-200-2-2-2-22i−2i0000−2i−2i2i2i00-22200002i−2i00000000000000
χ2322-22-2222-222-2-20000-2-2222-2-2-222200000000002-2-2-2200000000002-200000000
χ2422-22-2-222222-2-20000-2-2-2-2222-22220000000000-22-2-220000000000-2200000000
χ2522-2-22022022220000-2-200-2002-2-2-2002-2-220000002-220000002-2-220000000000
χ2622-2-22022022220000-2-200-2002-2-2-200-222-20000002-22000000-222-20000000000
χ2722-2-22022022222222-2-200-2002-222-2-20000222200-22-20000-2-200000000000000
χ2822-2-2202202222-2-2-2-2-2-200-2002-222220000-2-2-2-200-22-200002200000000000000
χ294444441-241-21122221-211111-2-200222222-1-1-1-1-2-20000000-1-1-1-1-1-10000000000
χ304444441-241-211-2-2-2-21-211111-2-200-2-2-2-2-2-21111-2-200000001111110000000000
χ31444444-214-21-2-20000-21-2-2-2-2-21100000000000011000222200000000-1-1-1-10000
χ32444444-214-21-2-20000-21-2-2-2-2-21100000000000011000-2-2-2-20000000011110000
χ3344444-41-2-41-21122221-2-1-11-1-1-2-20022-2-2-2-2-1-1-1-1220000000-1-111110000000000
χ3444444-41-2-41-211-2-2-2-21-2-1-11-1-1-2-200-2-22222111122000000011-1-1-1-10000000000
χ3544444-4-21-4-21-2-20000-2122-22211000000000000-1-100022-2-200000000-1-1110000
χ3644444-4-21-4-21-2-20000-2122-22211000000000000-1-1000-2-2220000000011-1-10000
χ37444-4-401-201-2-1-12i2i−2i−2i1-23-3-13-32200−2i2i2i−2i2i−2i−i−iii000000000i−i−ii−ii0000000000
χ38444-4-401-201-2-1-12i2i−2i−2i1-2-33-1-332200−2i2i−2i2i−2i2i−i−iii000000000i−ii−ii−i0000000000
χ39444-4-401-201-2-1-1−2i−2i2i2i1-23-3-13-322002i−2i−2i2i−2i2iii−i−i000000000−iii−ii−i0000000000
χ40444-4-401-201-2-1-1−2i−2i2i2i1-2-33-1-3322002i−2i2i−2i2i−2iii−i−i000000000−ii−ii−ii0000000000
χ4144-44-441-2-41-2-1-12i2i−2i−2i-12111-1-12-2002i−2i2i2i−2i−2i−i−iii-220000000−ii−i−iii0000000000
χ4244-44-441-2-41-2-1-1−2i−2i2i2i-12111-1-12-200−2i2i−2i−2i2i2iii−i−i-220000000i−iii−i−i0000000000
χ4344-44-44-21-4-212200002-1-2-2-222-110000000000001-10002-22-200000000-11-110000
χ4444-44-44-21-4-212200002-1-2-2-222-110000000000001-1000-22-22000000001-11-10000
χ4544-44-4-41-241-2-1-12i2i−2i−2i-12-1-11112-2002i−2i−2i−2i2i2i−i−iii2-20000000−iiii−i−i0000000000
χ4644-44-4-41-241-2-1-1−2i−2i2i2i-12-1-11112-200−2i2i2i2i−2i−2iii−i−i2-20000000i−i−i−iii0000000000
χ4744-44-4-4-214-212200002-122-2-2-2-11000000000000-110002-2-2200000000-111-10000
χ4844-44-4-4-214-212200002-122-2-2-2-11000000000000-11000-222-2000000001-1-110000
χ4944-4-4401-201-2112222-123-3-1-33-2200-2-22-2-22-1-1-1-100000000011-111-10000000000
χ5044-4-4401-201-2112222-12-33-13-3-2200-2-2-222-2-1-1-1-1000000000111-1-110000000000
χ5144-4-4401-201-211-2-2-2-2-123-3-1-33-220022-222-21111000000000-1-11-1-110000000000
χ5244-4-4401-201-211-2-2-2-2-12-33-13-3-2200222-2-221111000000000-1-1-111-10000000000
χ534-40000440-4-4002i2−2i22i2−2i2000000000-440000002i2−2i22i2−2i20000000000000000000000000
χ544-40000440-4-40022−22−22220000000004-400000022−22−22220000000000000000000000000
χ554-40000440-4-400−222222−220000000004-4000000−222222−220000000000000000000000000
χ564-40000440-4-400−2i22i2−2i22i2000000000-44000000−2i22i2−2i22i20000000000000000000000000
χ57888-8-80-420-42440000-4200400-2-20000000000000000000000000000000000000
χ5888-8-880-420-42-4-400004-2004002-20000000000000000000000000000000000000
χ598-800002-40-246i−6i4ζ−4ζ4ζ3−4ζ300000000000000000−2ζ2ζ−2ζ32ζ30000000000000000000000000
χ608-800002-40-246i−6i−4ζ4ζ−4ζ34ζ3000000000000000002ζ−2ζ2ζ3−2ζ30000000000000000000000000
χ618-800002-40-24−6i6i4ζ3−4ζ34ζ−4ζ00000000000000000−2ζ32ζ3−2ζ2ζ0000000000000000000000000
χ628-800002-40-24−6i6i−4ζ34ζ3−4ζ4ζ000000000000000002ζ3−2ζ32ζ−2ζ0000000000000000000000000
χ6316-160000-8408-40000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.