Finite Group Databasebeta

← Group #10828639

Character table — Group #10828639

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size111122222222224444444444444466668888888888888888888888121212121212161616161616161624242424242424244848
order122222344446664444444466121212124444244444661212121212121212121212121212224444881212242424242444444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-111-1-1-1-1-1-1-1-1-11111-1-11111111111-1-111-1-1-1-1-1-1-11111-1-1-1
χ31111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-1111
χ5111111111111111111-1-1-1-111111111111-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-1
χ6111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-111-1-1-111
χ7111111111111111111-1-1-1-1111111-1-1-1-11-1-1111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-111
χ8111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111111-1-1111-1-1
χ911111111111111-1-1-1-1111111111111111-1-11-1-111-1-111-1-1-1-1-1-111111111111-1-1-111-1-1-11-1-1-1-1-111-1
χ1011111111111111-1-1-1-111111111111111-1-1-1-111-1-111-1-1-1-1-1-1111111111111-11-1-1-1-1111-11-1-1-1-1-1-11
χ1111111111111111-1-1-1-11111111111-1-1-1-11-1-11-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11-1-1-111-1-11-111111-1-11
χ1211111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-11-1-1-1-111-11-1111111-1
χ1311111111111111-1-1-1-1-1-1-1-111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1111-1-111-11-1-1-1111-11
χ1411111111111111-1-1-1-1-1-1-1-11111111111-111-111-1-111-1-1-1-1-1-111-1-1-1-111-1-1-1-11-11111-1-11-11-1-111-11-1
χ1511111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1111-1111-1-1-11-1
χ1611111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-111-111-1-111-1-1-1-1-1-111-1-1-1-1-1-111111-11111-1-1-11-111-1-11-11
χ172222222-2-2-2-222222-2-2000022-2-2-2-2222200000000000022-2-2000000-2-20000000000000002-200000
χ182222222-2-2-2-222222-2-2000022-2-2-2-2-2-2-2-200000000000022-2-200000022000000000000000-2200000
χ192222222-2-2-2-2222-2-222000022-2-2-2-22222000000000000-2-222000000-2-2000000000000000-2200000
χ202222222-2-2-2-2222-2-222000022-2-2-2-2-2-2-2-2000000000000-2-222000000220000000000000002-200000
χ21222222-12222-1-1-122222222-1-1-1-1-1-10000222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000022-1-1-1-1-1-10000000000
χ22222222-12222-1-1-122222222-1-1-1-1-1-10000-222-2-2-2111111-1-1-1-111-1-1-1-1000000-2-2-1-111110000000000
χ23222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-100002-2-2222-1-1-1-1-1-1-1-1-1-1-1-11111000000-2-21111110000000000
χ24222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-10000-2-2-2-2-2-2111111-1-1-1-11111110000002211-1-1-1-10000000000
χ25222222-12222-1-1-1-2-2-2-22222-1-1-1-1-1-100002-2-22-2-2-1-111-1-1111111-1-1-1-10000002-211-1-1110000000000
χ26222222-12222-1-1-1-2-2-2-22222-1-1-1-1-1-10000-2-2-2-22211-1-1111111-1-1-1-1-1-1000000-221111-1-10000000000
χ27222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-100002222-2-2-1-111-1-11111111111000000-22-1-111-1-10000000000
χ28222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-10000-222-22211-1-1111111-1-111110000002-2-1-1-1-1110000000000
χ292222-2-222-22-222200000000-2-22-22-222-2-200002-200-2-20000002200002-200000000000020-20000000
χ302222-2-222-22-222200000000-2-22-22-222-2-20000-220022000000-2-200002-2000000000000-2020000000
χ312222-2-222-22-222200000000-2-22-22-2-2-22200002-200-2-2000000220000-22000000000000-2020000000
χ322222-2-222-22-222200000000-2-22-22-2-2-2220000-220022000000-2-20000-2200000000000020-20000000
χ332222-2-22-22-2222200000000-2-2-22-2222-2-2200-2002200-2-20000000000-220000000000000200000-200
χ342222-2-22-22-2222200000000-2-2-22-2222-2-2-200200-2-200220000000000-220000000000000-200000200
χ352222-2-22-22-2222200000000-2-2-22-22-2-222200-2002200-2-200000000002-20000000000000-200000200
χ362222-2-22-22-2222200000000-2-2-22-22-2-222-200200-2-2002200000000002-20000000000000200000-200
χ3722-2-2-2222-2-22-22-22i−2i2i−2i22-2-2-22-222-2000002i−2i0000000002i−2i2i−2i0022-2-2000000002i−2i00000000000000
χ3822-2-2-2222-2-22-22-22i−2i2i−2i-2-222-22-222-200000−2i2i0000000002i−2i2i−2i00-2-22200000000−2i2i00000000000000
χ3922-2-2-2222-2-22-22-2−2i2i−2i2i22-2-2-22-222-200000−2i2i000000000−2i2i−2i2i0022-2-200000000−2i2i00000000000000
χ4022-2-2-2222-2-22-22-2−2i2i−2i2i-2-222-22-222-2000002i−2i000000000−2i2i−2i2i00-2-222000000002i−2i00000000000000
χ4122-2-2-222-222-2-22-22i−2i−2i2i0000-222-2-2200000000000000002i−2i−2i2i0000000022-2-200000000000002i−2i000
χ4222-2-2-222-222-2-22-22i−2i−2i2i0000-222-2-2200000000000000002i−2i−2i2i00000000-2-2220000000000000−2i2i000
χ4322-2-2-222-222-2-22-2−2i2i2i−2i0000-222-2-220000000000000000−2i2i2i−2i0000000022-2-20000000000000−2i2i000
χ4422-2-2-222-222-2-22-2−2i2i2i−2i0000-222-2-220000000000000000−2i2i2i−2i00000000-2-22200000000000002i−2i000
χ4522-2-2-22-12-2-221-112i−2i2i−2i22-2-21-11-1-11000002i−2i000−i3i33−3−i3i3−ii−ii3−3-1-11100000000−ii−i3i33−30000000000
χ4622-2-2-22-12-2-221-112i−2i2i−2i22-2-21-11-1-11000002i−2i000i3−i3−33i3−i3−ii−ii−33-1-11100000000−iii3−i3−330000000000
χ4722-2-2-22-12-2-221-112i−2i2i−2i-2-2221-11-1-1100000−2i2i000−i3i33−3−i3i3−ii−ii3−311-1-100000000i−ii3−i3−330000000000
χ4822-2-2-22-12-2-221-112i−2i2i−2i-2-2221-11-1-1100000−2i2i000i3−i3−33i3−i3−ii−ii−3311-1-100000000i−i−i3i33−30000000000
χ4922-2-2-22-12-2-221-11−2i2i−2i2i22-2-21-11-1-1100000−2i2i000−i3i3−33−i3i3i−ii−i−33-1-11100000000i−i−i3i3−330000000000
χ5022-2-2-22-12-2-221-11−2i2i−2i2i22-2-21-11-1-1100000−2i2i000i3−i33−3i3−i3i−ii−i3−3-1-11100000000i−ii3−i33−30000000000
χ5122-2-2-22-12-2-221-11−2i2i−2i2i-2-2221-11-1-11000002i−2i000−i3i3−33−i3i3i−ii−i−3311-1-100000000−iii3−i33−30000000000
χ5222-2-2-22-12-2-221-11−2i2i−2i2i-2-2221-11-1-11000002i−2i000i3−i33−3i3−i3i−ii−i3−311-1-100000000−ii−i3i3−330000000000
χ53444444-2-4-4-4-4-2-2-244-4-40000-2-222220000000000000000-2-222000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-2-4-4440000-2-22222000000000000000022-2-2000000000000000000000000000000
χ554444-4-4-24-44-4-2-2-20000000022-22-22000000004-40022000000-2-20000000000000000000000000000
χ564444-4-4-24-44-4-2-2-20000000022-22-2200000000-4400-2-2000000220000000000000000000000000000
χ574444-4-4-2-44-44-2-2-200000000222-22-20000400-400-2-200220000000000000000000000000000000000
χ584444-4-4-2-44-44-2-2-200000000222-22-20000-4004002200-2-20000000000000000000000000000000000
χ5944-4-44-4444-4-4-44-4000000004-4-4-44400000000000000000000000000000000000000000000000000
χ6044-4-44-44-4-444-44-4000000004-444-4-400000000000000000000000000000000000000000000000000
χ6144-4-44-4-244-4-42-2200000000-2222-2-200000000000023−23000000−23230000000000000000000000000000
χ6244-4-44-4-244-4-42-2200000000-2222-2-2000000000000−232300000023−230000000000000000000000000000
χ6344-4-44-4-2-4-4442-2200000000-22-2-2220000000000−2i32i3002i3−2i30000000000000000000000000000000000
χ6444-4-44-4-2-4-4442-2200000000-22-2-22200000000002i3−2i300−2i32i30000000000000000000000000000000000
χ6544-4-4-44-2-444-42-224i−4i−4i4i00002-2-222-20000000000000000−2i2i2i−2i000000000000000000000000000000
χ6644-4-4-44-2-444-42-22−4i4i4i−4i00002-2-222-200000000000000002i−2i−2i2i000000000000000000000000000000
χ674-44-40040000-4-4400002-22-2000000004i−4i0000000000000000002-22-2002i−2i2i−2i000000000000000000
χ684-44-40040000-4-4400002-22-200000000−4i4i0000000000000000002-22-200−2i2i−2i2i000000000000000000
χ694-44-40040000-4-440000-22-22000000004i−4i000000000000000000-22-2200−2i2i−2i2i000000000000000000
χ704-44-40040000-4-440000-22-2200000000−4i4i000000000000000000-22-22002i−2i2i−2i000000000000000000
χ714-4-4400400004-4-400002-2-220000004i−4i000000000000000000002-2-22002i−2i−2i2i000000000000000000
χ724-4-4400400004-4-400002-2-22000000−4i4i000000000000000000002-2-2200−2i2i2i−2i000000000000000000
χ734-4-4400400004-4-40000-222-20000004i−4i00000000000000000000-222-200−2i2i2i−2i000000000000000000
χ744-4-4400400004-4-40000-222-2000000−4i4i00000000000000000000-222-2002i−2i−2i2i000000000000000000
χ758-88-800-4000044-400004-44-40000000000000000000000000000-22-22000000000000000000000000
χ768-88-800-4000044-40000-44-4400000000000000000000000000002-22-2000000000000000000000000
χ778-8-8800-40000-44400004-4-440000000000000000000000000000-222-2000000000000000000000000
χ788-8-8800-40000-4440000-444-400000000000000000000000000002-2-22000000000000000000000000

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