Finite Group Databasebeta

← Group #10831853

Character table — Group #10831853

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222224444444444444466668888888888888888888888121212121212161616161616161624242424242424244848
order12222222223666224444446666664444444444661212121212121212121212121212222244441212121212124444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-11-1-11-1-111-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-111-1-111
χ5111111111111111111-1-1-1-111111111111111-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ6111111111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111-1-11-1-1-1-111
χ7111111111111111111-1-1-1-1111111-1-1-1-11111-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-111-11111-1-1
χ911111111111111-1-1-1-1111111111111111-11-1-1-1-1-1-1-111-1-1111111-1-11111111-1-1-111-1-1-11-1-11-1-1-11-1
χ1011111111111111-1-1-1-111111111111111-11-11-1-1-1-1-1-1-1-1111111-1-111111111-11-1-1-1-111-1-11-1-11-1-1-11
χ1111111111111111-1-1-1-11111111111-1-1-1-11-11-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11-1-1-111-1-11-111-1111-11
χ1211111111111111-1-1-1-11111111111-1-1-1-1-11-11-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-11-1-1-1-11111-111-1111-1
χ1311111111111111-1-1-1-1-1-1-1-111111111111-11-111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111-1111-1-111-11-1-11-111-11
χ1411111111111111-1-1-1-1-1-1-1-11111111111-11-1111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1111-11111-1-1-1-11-1-11111-1
χ1511111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-11-111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1111-1-1111-111-11-1-11-1
χ1611111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11-11111-1-111-111-1-1-1-11
χ172222222222-1-1-1-122222222-1-1-1-1-1-10000222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-10000000000
χ182222222222-1-1-1-122222222-1-1-1-1-1-10000-2-2-2-222-1-1-1-11111-1-1-1-11111000000-2-2-1-111110000000000
χ192222222222-1-1-1-12222-2-2-2-2-1-1-1-1-1-100002222-2-2-1-1-1-1-1-1-1-11111-1-1-1-1000000-2-21111110000000000
χ202222222222-1-1-1-12222-2-2-2-2-1-1-1-1-1-10000-2-2-2-2-2-2-1-1-1-11111111111110000002211-1-1-1-10000000000
χ212222222222-1-1-1-1-2-2-2-22222-1-1-1-1-1-100002-22-2-2-21111-1-111-1-1-1-1-1-1110000002-211-1-1110000000000
χ222222222222-1-1-1-1-2-2-2-22222-1-1-1-1-1-10000-22-22-2-2111111-1-1-1-1-1-111-1-1000000-221111-1-10000000000
χ232222222222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-100002-22-2221111-1-1111111-1-111000000-22-1-111-1-10000000000
χ242222222222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-10000-22-2222111111-1-1111111-1-10000002-2-1-1-1-1110000000000
χ2522222-2-2-22-22222000000002-2-22-2-222-2-2020-20000000022000000-2-200002-20000000000200-20000
χ2622222-2-2-22-22222000000002-2-22-2-222-2-20-20200000000-2-20000002200002-20000000000-20020000
χ2722222-2-2-22-22222000000002-2-22-2-2-2-222020-20000000022000000-2-20000-220000000000-20020000
χ2822222-2-2-22-22222000000002-2-22-2-2-2-2220-20200000000-2-2000000220000-220000000000200-20000
χ292222-22-2-2-22222200000000-22-2-22-222-2-220-2000000022000000-2-2000000-22000000000200-200000
χ302222-22-2-2-22222200000000-22-2-22-222-2-2-2020000000-2-200000022000000-22000000000-200200000
χ312222-22-2-2-22222200000000-22-2-22-2-2-22220-2000000022000000-2-20000002-2000000000-200200000
χ322222-22-2-2-22222200000000-22-2-22-2-2-222-2020000000-2-2000000220000002-2000000000200-200000
χ332222-2-222-2-2222222-2-20000-2-22-2-22222200000022-2-20000000000000000-2-200000000-2002000000
χ342222-2-222-2-2222222-2-20000-2-22-2-22-2-2-2-200000022-2-200000000000000002200000000200-2000000
χ352222-2-222-2-22222-2-2220000-2-22-2-222222000000-2-2220000000000000000-2-200000000200-2000000
χ362222-2-222-2-22222-2-2220000-2-22-2-22-2-2-2-2000000-2-22200000000000000002200000000-2002000000
χ3722-2-222-22-2-222-2-22-22-20000222-2-2-200000000002-22-200000000000022-2-200000000000000002-200
χ3822-2-222-22-2-222-2-22-22-20000222-2-2-200000000002-22-2000000000000-2-2220000000000000000-2200
χ3922-2-222-22-2-222-2-2-22-220000222-2-2-20000000000-22-2200000000000022-2-20000000000000000-2200
χ4022-2-222-22-2-222-2-2-22-220000222-2-2-20000000000-22-22000000000000-2-22200000000000000002-200
χ4122-2-2-2-2-222222-2-22-2-222i2i−2i−2i-2-2222-2000000002i−2i2-2-2200002i2i−2i−2i0000000000002i−2i00000000000000
χ4222-2-2-2-2-222222-2-22-2-22−2i−2i2i2i-2-2222-200000000−2i2i2-2-220000−2i−2i2i2i000000000000−2i2i00000000000000
χ4322-2-2-2-2-222222-2-2-222-22i2i−2i−2i-2-2222-200000000−2i2i-222-200002i2i−2i−2i000000000000−2i2i00000000000000
χ4422-2-2-2-2-222222-2-2-222-2−2i−2i2i2i-2-2222-2000000002i−2i-222-20000−2i−2i2i2i0000000000002i−2i00000000000000
χ4522-2-2-2-2-2222-1-1112-2-222i2i−2i−2i11-1-1-11000000002i−2i-111-13−33−3−i−iii3−33−300000000−ii−i3i3−i3i30000000000
χ4622-2-2-2-2-2222-1-1112-2-222i2i−2i−2i11-1-1-11000000002i−2i-111-1−33−33−i−iii−33−3300000000−iii3−i3i3−i30000000000
χ4722-2-2-2-2-2222-1-1112-2-22−2i−2i2i2i11-1-1-1100000000−2i2i-111-13−33−3ii−i−i3−33−300000000i−ii3−i3i3−i30000000000
χ4822-2-2-2-2-2222-1-1112-2-22−2i−2i2i2i11-1-1-1100000000−2i2i-111-1−33−33ii−i−i−33−3300000000i−i−i3i3−i3i30000000000
χ4922-2-2-2-2-2222-1-111-222-22i2i−2i−2i11-1-1-1100000000−2i2i1-1-113−3−33−i−iii3−3−3300000000i−i−i3i3i3−i30000000000
χ5022-2-2-2-2-2222-1-111-222-22i2i−2i−2i11-1-1-1100000000−2i2i1-1-11−333−3−i−iii−333−300000000i−ii3−i3−i3i30000000000
χ5122-2-2-2-2-2222-1-111-222-2−2i−2i2i2i11-1-1-11000000002i−2i1-1-113−3−33ii−i−i3−3−3300000000−iii3−i3−i3i30000000000
χ5222-2-2-2-2-2222-1-111-222-2−2i−2i2i2i11-1-1-11000000002i−2i1-1-11−333−3ii−i−i−333−300000000−ii−i3i3i3−i30000000000
χ5344444-4-4-44-4-2-2-2-200000000-222-2220000040-400000000-2-200000022000000000000000000000000
χ5444444-4-4-44-4-2-2-2-200000000-222-22200000-4040000000022000000-2-2000000000000000000000000
χ554444-44-4-4-44-2-2-2-2000000002-222-22000040-40000000-2-20000002200000000000000000000000000
χ564444-44-4-4-44-2-2-2-2000000002-222-220000-404000000022000000-2-200000000000000000000000000
χ574444-4-444-4-4-2-2-2-244-4-4000022-222-20000000000-2-222000000000000000000000000000000000000
χ584444-4-444-4-4-2-2-2-2-4-444000022-222-2000000000022-2-2000000000000000000000000000000000000
χ5944-4-444-44-4-4-2-2224-44-40000-2-2-22220000000000-22-22000000000000000000000000000000000000
χ6044-4-444-44-4-4-2-222-44-440000-2-2-222200000000002-22-2000000000000000000000000000000000000
χ6144-4-44-44-4-4444-4-4000000004-4-4-44400000000000000000000000000000000000000000000000000
χ6244-4-44-44-4-44-2-22200000000-2222-2-20000000000000023−23000000−232300000000000000000000000000
χ6344-4-44-44-4-44-2-22200000000-2222-2-200000000000000−232300000023−2300000000000000000000000000
χ6444-4-4-444-44-444-4-400000000-44-44-4400000000000000000000000000000000000000000000000000
χ6544-4-4-444-44-4-2-222000000002-22-22-2000000000000000023−23000000−2323000000000000000000000000
χ6644-4-4-444-44-4-2-222000000002-22-22-20000000000000000−232300000023−23000000000000000000000000
χ674-44-40000004-44-400002i−2i2i−2i000000004i−4i000000000000002i−2i2i−2i00002-22-200000000000000000000
χ684-44-40000004-44-400002i−2i2i−2i00000000−4i4i000000000000002i−2i2i−2i0000-22-2200000000000000000000
χ694-44-40000004-44-40000−2i2i−2i2i000000004i−4i00000000000000−2i2i−2i2i0000-22-2200000000000000000000
χ704-44-40000004-44-40000−2i2i−2i2i00000000−4i4i00000000000000−2i2i−2i2i00002-22-200000000000000000000
χ714-4-440000004-4-4400002-2-220000004-400000000000000002-2-2200002-2-2200000000000000000000
χ724-4-440000004-4-4400002-2-22000000-4400000000000000002-2-220000-222-200000000000000000000
χ734-4-440000004-4-440000-222-20000004-40000000000000000-222-20000-222-200000000000000000000
χ744-4-440000004-4-440000-222-2000000-440000000000000000-222-200002-2-2200000000000000000000
χ758-88-8000000-44-4400004i−4i4i−4i000000000000000000000000−2i2i−2i2i0000000000000000000000000000
χ768-88-8000000-44-440000−4i4i−4i4i0000000000000000000000002i−2i2i−2i0000000000000000000000000000
χ778-8-88000000-444-400004-4-44000000000000000000000000-222-20000000000000000000000000000
χ788-8-88000000-444-40000-444-40000000000000000000000002-2-220000000000000000000000000000

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