Finite Group Databasebeta

← Group #10828666

Character table — Group #10828666

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size111122222222224444444444888888888888888888888888121212121616161616161616242424242424242424244848
order122222344446664444661212121224444444661212121212121212121212121212224488121224242424244444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-111111111-1-111-1-1-1-1-1-111-1-11111-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-11111-1-111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1111111-1-1
χ911111111111111-1-1-1-111111111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-111111-11111-1-1-1-1-1-11111-1-11-1
χ1011111111111111-1-1-1-111111111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-11111-1-1-1-111-11
χ1111111111111111-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1-1-111111111-11-1-1-1-111-1-1-1-111-1-111-11
χ1211111111111111-1-1-1-111111111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-11-1-1-1-1111111-1-111-1-11-1
χ1311111111111111-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1111-1-11111-1-1-1-111-1-1-11
χ1411111111111111-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1111-1-111-1-11111-1-1111-1
χ1511111111111111-1-1-1-1111111-1-111-1-111-1-111-1-1-1-1-1-111111111111-1-1-111-1-111-1-1-1-1-1-1111-1
χ1611111111111111-1-1-1-1111111-1-111-1-111-1-111-1-1-1-1-1-1111111-1-1-1-11-1-1-111-1-1-1-1111111-1-1-11
χ172222222-2-2-2-222222-2-222-2-2-2-20000000000000022-2-200000022-2-200000000002-200000000
χ182222222-2-2-2-222222-2-222-2-2-2-20000000000000022-2-2000000-2-2220000000000-2200000000
χ192222222-2-2-2-2222-2-22222-2-2-2-200000000000000-2-22200000022-2-20000000000-2200000000
χ202222222-2-2-2-2222-2-22222-2-2-2-200000000000000-2-222000000-2-22200000000002-200000000
χ21222222-12222-1-1-12222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-1000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111110000-2-2111111000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-1-2-2-2-22222111111-1-1-1-111-1-1-1-10000-2-2-1-11111000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111-1-1-1-111111100002211-1-1-1-1000000000000
χ25222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-122-2-222-2-2-1-111-1-1111111111100002-2-1-1-1-111000000000000
χ26222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-122-2-2-2-222-1-111-1-1111111-1-1-1-10000-221111-1-1000000000000
χ27222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1-2-22222-2-211-1-1111111-1-111110000-22-1-111-1-1000000000000
χ28222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-1-2-222-2-22211-1-1111111-1-1-1-1-1-100002-211-1-111000000000000
χ292222-2-222-22-22220000-2-22-22-2002-200000022000000-2-200002-22-2000000002-20000000000
χ302222-2-222-22-22220000-2-22-22-2002-200000022000000-2-20000-22-2200000000-220000000000
χ312222-2-222-22-22220000-2-22-22-200-22000000-2-20000002200002-22-200000000-220000000000
χ322222-2-222-22-22220000-2-22-22-200-22000000-2-2000000220000-22-22000000002-20000000000
χ332222-2-22-22-222220000-2-2-22-222-20000002200-2-200000000002-2-22000000000000-22000000
χ342222-2-22-22-222220000-2-2-22-222-20000002200-2-20000000000-222-20000000000002-2000000
χ352222-2-22-22-222220000-2-2-22-22-22000000-2-2002200000000002-2-220000000000002-2000000
χ362222-2-22-22-222220000-2-2-22-22-22000000-2-200220000000000-222-2000000000000-22000000
χ3722-2-2-2222-2-22-22-22i−2i2i−2i-22-222-200002i−2i2-20000002i−2i2i−2i0022-2-20000002i−2i0000000000000000
χ3822-2-2-2222-2-22-22-22i−2i2i−2i-22-222-20000−2i2i-220000002i−2i2i−2i00-2-222000000−2i2i0000000000000000
χ3922-2-2-2222-2-22-22-2−2i2i−2i2i-22-222-200002i−2i-22000000−2i2i−2i2i00-2-2220000002i−2i0000000000000000
χ4022-2-2-2222-2-22-22-2−2i2i−2i2i-22-222-20000−2i2i2-2000000−2i2i−2i2i0022-2-2000000−2i2i0000000000000000
χ4122-2-2-222-222-2-22-22i−2i−2i2i-222-2-22000000000000002i−2i−2i2i0000000000000000000000002i−2i2-200
χ4222-2-2-222-222-2-22-22i−2i−2i2i-222-2-22000000000000002i−2i−2i2i000000000000000000000000−2i2i-2200
χ4322-2-2-222-222-2-22-2−2i2i2i−2i-222-2-2200000000000000−2i2i2i−2i0000000000000000000000002i−2i-2200
χ4422-2-2-222-222-2-22-2−2i2i2i−2i-222-2-2200000000000000−2i2i2i−2i000000000000000000000000−2i2i2-200
χ4522-2-2-22-12-2-221-112i−2i2i−2i1-11-1-1100002i−2i2-2−i3i33−3−i3i3−ii−ii3−3-1-111000000−ii3−3−i3i3000000000000
χ4622-2-2-22-12-2-221-112i−2i2i−2i1-11-1-1100002i−2i2-2i3−i3−33i3−i3−ii−ii−33-1-111000000−ii−33i3−i3000000000000
χ4722-2-2-22-12-2-221-112i−2i2i−2i1-11-1-110000−2i2i-22−i3i33−3−i3i3−ii−ii3−311-1-1000000i−i−33i3−i3000000000000
χ4822-2-2-22-12-2-221-112i−2i2i−2i1-11-1-110000−2i2i-22i3−i3−33i3−i3−ii−ii−3311-1-1000000i−i3−3−i3i3000000000000
χ4922-2-2-22-12-2-221-11−2i2i−2i2i1-11-1-1100002i−2i-22−i3i3−33−i3i3i−ii−i−3311-1-1000000−ii3−3i3−i3000000000000
χ5022-2-2-22-12-2-221-11−2i2i−2i2i1-11-1-1100002i−2i-22i3−i33−3i3−i3i−ii−i3−311-1-1000000−ii−33−i3i3000000000000
χ5122-2-2-22-12-2-221-11−2i2i−2i2i1-11-1-110000−2i2i2-2−i3i3−33−i3i3i−ii−i−33-1-111000000i−i−33−i3i3000000000000
χ5222-2-2-22-12-2-221-11−2i2i−2i2i1-11-1-110000−2i2i2-2i3−i33−3i3−i3i−ii−i3−3-1-111000000i−i3−3i3−i3000000000000
χ53444444-2-4-4-4-4-2-2-244-4-4-2-2222200000000000000-2-222000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-2-4-444-2-222220000000000000022-2-2000000000000000000000000000000
χ554444-4-4-24-44-4-2-2-2000022-22-22004-4000000-2-2000000220000000000000000000000000000
χ564444-4-4-24-44-4-2-2-2000022-22-2200-4400000022000000-2-20000000000000000000000000000
χ574444-4-4-2-44-44-2-2-20000222-22-24-4000000-2-200220000000000000000000000000000000000
χ584444-4-4-2-44-44-2-2-20000222-22-2-440000002200-2-20000000000000000000000000000000000
χ5944-4-44-4444-4-4-44-400004-4-4-444000000000000000000000000000000000000000000000000
χ6044-4-44-44-4-444-44-400004-444-4-4000000000000000000000000000000000000000000000000
χ6144-4-44-4-244-4-42-220000-2222-2-2000000000023−23000000−23230000000000000000000000000000
χ6244-4-44-4-244-4-42-220000-2222-2-20000000000−232300000023−230000000000000000000000000000
χ6344-4-44-4-2-4-4442-220000-22-2-22200000000−2i32i3002i3−2i30000000000000000000000000000000000
χ6444-4-44-4-2-4-4442-220000-22-2-222000000002i3−2i300−2i32i30000000000000000000000000000000000
χ6544-4-4-44-2-444-42-224i−4i−4i4i2-2-222-200000000000000−2i2i2i−2i000000000000000000000000000000
χ6644-4-4-44-2-444-42-22−4i4i4i−4i2-2-222-2000000000000002i−2i−2i2i000000000000000000000000000000
χ678-88-800800008-8-80000000000000000000000000000000000000000000000000000000000
χ688-88-800-40000-444000000000000000000000000000000−2i32i3−2i32i3000000000000000000000000
χ698-88-800-40000-4440000000000000000000000000000002i3−2i32i3−2i3000000000000000000000000
χ708-8-880080000-8-880000000000000000000000000000000000000000000000000000000000
χ718-8-8800-4000044-4000000000000000000000000000000−2i32i32i3−2i3000000000000000000000000
χ728-8-8800-4000044-40000000000000000000000000000002i3−2i3−2i32i3000000000000000000000000

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