Finite Group Databasebeta

← Group #10896451

Character table — Group #10896451

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222224444444444444444444444444488888888888888888888888888888888242424242424242448484848
order12442223444612126668888888812121224242424242424242424242422444466668888121212121212121224242424242424242424444488884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-1-1-111111111111-1-1-1-11-11-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-11-11-1
χ6111111111111111111111-1-1-1-111111111111-1-1-1-11-11-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-11-11
χ7111111111111111111111-1-1-1-111111111111-1-1-1-1-11-11-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-11-11
χ8111111111111111111111-1-1-1-111111111111-1-1-1-1-11-11-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111-11-1
χ911111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ1011111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ1111111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-111
χ1211111111111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-11111-1-111-1-1
χ1311111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-11111-1-11111-1-1-1-11111-1-11111-1-1-1-11-1-11
χ1411111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-11111-111-1
χ1511111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-11111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1-111-1
χ1611111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111-1-11
χ172222222-1222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ182222222-1222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2221111-2-2-2-21111-1-1-1-111111111-1-1000000000000
χ192222222-1222-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111112-22-2-2-2-1-11122-2-2-1-1111111-1-1-1-1111111000000000000
χ202222222-1222-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111-22-22-2-211-1-1-2-22211-1-111111111-1-1-1-111000000000000
χ212222222-1222-1-1-1-1-1-1-2-2-2-22222-1-1-111111111-1-1-1-12222-2-2-1-1-1-1-2-2-2-2-1-1-1-1111111111111-1-1000000000000
χ222222222-1222-1-1-1-1-1-1-2-2-2-22222-1-1-111111111-1-1-1-1-2-2-2-2-2-21111222211111111-1-1-1-1-1-1-1-1-1-1000000000000
χ232222222-1222-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-11111111111112-22-222-1-111-2-222-1-111-1-1-1-11111-1-1-1-111000000000000
χ242222222-1222-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1111111111111-22-222211-1-122-2-211-1-1-1-1-1-1-1-1-1-1111111000000000000
χ252222-2-222-22-2222-2-2222-2-222-2-2-2-222222-2-2-2-2222200002-200000000000022-2-200000000-2-2000000000000
χ262222-2-222-22-2222-2-2222-2-2-2-222-2-222222-2-2-2-2-2-2-2-20000-22000000000000-2-2220000000022000000000000
χ272222-2-222-22-2222-2-22-2-22222-2-2-2-22-2-2-2-2222222220000-22000000000000-2-22200000000-2-2000000000000
χ282222-2-222-22-2222-2-22-2-222-2-222-2-22-2-2-2-22222-2-2-2-200002-200000000000022-2-20000000022000000000000
χ292222-2-22-1-22-2-1-1-111-122-2-222-2-211-1-1-1-1-11111-1-1-1-100002-2−i3i3−i3i30000−i3i3−i3i3-1-111−i3−i3i3i3−i3−i3i3i311000000000000
χ302222-2-22-1-22-2-1-1-111-122-2-222-2-211-1-1-1-1-11111-1-1-1-100002-2i3−i3i3−i30000i3−i3i3−i3-1-111i3i3−i3−i3i3i3−i3−i311000000000000
χ312222-2-22-1-22-2-1-1-111-122-2-2-2-22211-1-1-1-1-1111111110000-22−i3i3i3−i30000−i3i3i3−i311-1-1−i3−i3i3i3i3i3−i3−i3-1-1000000000000
χ322222-2-22-1-22-2-1-1-111-122-2-2-2-22211-1-1-1-1-1111111110000-22i3−i3−i3i30000i3−i3−i3i311-1-1i3i3−i3−i3−i3−i3i3i3-1-1000000000000
χ332222-2-22-1-22-2-1-1-111-1-2-22222-2-211-11111-1-1-1-1-1-1-1-10000-22−i3i3−i3i30000−i3i3−i3i311-1-1i3i3−i3−i3i3i3−i3−i311000000000000
χ342222-2-22-1-22-2-1-1-111-1-2-22222-2-211-11111-1-1-1-1-1-1-1-10000-22i3−i3i3−i30000i3−i3i3−i311-1-1−i3−i3i3i3−i3−i3i3i311000000000000
χ352222-2-22-1-22-2-1-1-111-1-2-222-2-22211-11111-1-1-1-1111100002-2−i3i3i3−i30000−i3i3i3−i3-1-111i3i3−i3−i3−i3−i3i3i3-1-1000000000000
χ362222-2-22-1-22-2-1-1-111-1-2-222-2-22211-11111-1-1-1-1111100002-2i3−i3−i3i30000i3−i3−i3i3-1-111−i3−i3i3i3i3i3−i3−i3-1-1000000000000
χ3722-2-22222-2-2-22-2-22222i−2i2i−2i0000-2-2-22i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000002-2002i−2i000000
χ3822-2-22222-2-2-22-2-22222i−2i2i−2i0000-2-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000-2200−2i2i000000
χ3922-2-22222-2-2-22-2-2222−2i2i−2i2i0000-2-2-2−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000002-200−2i2i000000
χ4022-2-22222-2-2-22-2-2222−2i2i−2i2i0000-2-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000-22002i−2i000000
χ4122-2-22-2-2222-22-2-22-2-200002-22-22-220000000022-2-222-2-20022220000-2-2-2-20000000000002-2000000000000
χ4222-2-22-2-2222-22-2-22-2-200002-22-22-220000000022-2-2-2-22200-2-2-2-2000022220000000000002-2000000000000
χ4322-2-22-2-2222-22-2-22-2-20000-22-222-2200000000-2-2222-2-220022-2-20000-2-222000000000000-22000000000000
χ4422-2-22-2-2222-22-2-22-2-20000-22-222-2200000000-2-222-222-200-2-222000022-2-2000000000000-22000000000000
χ4522-2-22-2-2-122-2-111-11100002-22-2-11-13−33−33−33−3-1-11122-2-200-1-1-1-1000011113−33−33−33−33−33−3-11000000000000
χ4622-2-22-2-2-122-2-111-11100002-22-2-11-13−33−33−33−3-1-111-2-2220011110000-1-1-1-13−33−3−33−33−33−33-11000000000000
χ4722-2-22-2-2-122-2-111-11100002-22-2-11-1−33−33−33−33-1-11122-2-200-1-1-1-100001111−33−33−33−33−33−33-11000000000000
χ4822-2-22-2-2-122-2-111-11100002-22-2-11-1−33−33−33−33-1-111-2-2220011110000-1-1-1-1−33−333−33−33−33−3-11000000000000
χ4922-2-22-2-2-122-2-111-1110000-22-22-11-13−33−33−33−311-1-12-2-2200-1-111000011-1-1−33−333−33−3−33−331-1000000000000
χ5022-2-22-2-2-122-2-111-1110000-22-22-11-13−33−33−33−311-1-1-222-20011-1-10000-1-111−33−33−33−333−33−31-1000000000000
χ5122-2-22-2-2-122-2-111-1110000-22-22-11-1−33−33−33−3311-1-12-2-2200-1-111000011-1-13−33−3−33−333−33−31-1000000000000
χ5222-2-22-2-2-122-2-111-1110000-22-22-11-1−33−33−33−3311-1-1-222-20011-1-10000-1-1113−33−33−33−3−33−331-1000000000000
χ5322-2-2-22-22-2222-2-2-22-200002-2-22-2220000000022-2-200000000002i−2i2i−2i000000002i−2i−2i2i2i−2i−2i2i-22000000000000
χ5422-2-2-22-22-2222-2-2-22-200002-2-22-2220000000022-2-20000000000−2i2i−2i2i00000000−2i2i2i−2i−2i2i2i−2i-22000000000000
χ5522-2-2-22-22-2222-2-2-22-20000-222-2-22200000000-2-22200000000002i−2i−2i2i000000002i−2i−2i2i−2i2i2i−2i2-2000000000000
χ5622-2-2-22-22-2222-2-2-22-20000-222-2-22200000000-2-2220000000000−2i2i2i−2i00000000−2i2i2i−2i2i−2i−2i2i2-2000000000000
χ5722-2-2-22-2-1-222-1111-1100002-2-221-1-13−33−3−33−33-1-111000000−i3i3−i3i32i−2i2i−2ii3−i3i3−i33−3−33−iii−i−iii−i1-1000000000000
χ5822-2-2-22-2-1-222-1111-1100002-2-221-1-13−33−3−33−33-1-111000000i3−i3i3−i3−2i2i−2i2i−i3i3−i3i33−3−33i−i−iii−i−ii1-1000000000000
χ5922-2-2-22-2-1-222-1111-1100002-2-221-1-1−33−333−33−3-1-111000000−i3i3−i3i3−2i2i−2i2ii3−i3i3−i3−333−3i−i−iii−i−ii1-1000000000000
χ6022-2-2-22-2-1-222-1111-1100002-2-221-1-1−33−333−33−3-1-111000000i3−i3i3−i32i−2i2i−2i−i3i3−i3i3−333−3−iii−i−iii−i1-1000000000000
χ6122-2-2-22-2-1-222-1111-110000-222-21-1-13−33−3−33−3311-1-1000000−i3i3i3−i32i−2i−2i2ii3−i3−i3i3−333−3−iii−ii−i−ii-11000000000000
χ6222-2-2-22-2-1-222-1111-110000-222-21-1-13−33−3−33−3311-1-1000000i3−i3−i3i3−2i2i2i−2i−i3i3i3−i3−333−3i−i−ii−iii−i-11000000000000
χ6322-2-2-22-2-1-222-1111-110000-222-21-1-1−33−333−33−311-1-1000000−i3i3i3−i3−2i2i2i−2ii3−i3−i3i33−3−33i−i−ii−iii−i-11000000000000
χ6422-2-2-22-2-1-222-1111-110000-222-21-1-1−33−333−33−311-1-1000000i3−i3−i3i32i−2i−2i2i−i3i3i3−i33−3−33−iii−ii−i−ii-11000000000000
χ6522-2-2-2-2222-222-2-2-2-222i−2i−2i2i000022-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000002-2002i−2i0000
χ6622-2-2-2-2222-222-2-2-2-222i−2i−2i2i000022-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000-2200−2i2i0000
χ6722-2-2-2-2222-222-2-2-2-22−2i2i2i−2i000022-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000002-200−2i2i0000
χ6822-2-2-2-2222-222-2-2-2-22−2i2i2i−2i000022-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000-22002i−2i0000
χ6944444-4-44-4-444444-4-400000000-44-400000000000000000000000000000000000000000000000000000000
χ7044444-4-4-2-4-44-2-2-2-222000000002-22−2i32i32i3−2i3−2i32i32i3−2i3000000000000000000000000000000000000000000000000
χ7144444-4-4-2-4-44-2-2-2-222000000002-222i3−2i3−2i32i32i3−2i3−2i32i3000000000000000000000000000000000000000000000000
χ724444-44-444-4-4444-44-4000000004-4-400000000000000000000000000000000000000000000000000000000
χ734444-44-4-24-4-4-2-2-22-2200000000-222−2i32i32i3−2i32i3−2i3−2i32i3000000000000000000000000000000000000000000000000
χ744444-44-4-24-4-4-2-2-22-2200000000-2222i3−2i3−2i32i3−2i32i32i3−2i3000000000000000000000000000000000000000000000000
χ7544-4-4444-2-4-4-4-222-2-2-24i−4i4i−4i0000222−2i−2i2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ7644-4-4444-2-4-4-4-222-2-2-2−4i4i−4i4i00002222i2i−2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ7744-4-4-4-44-24-44-22222-24i−4i−4i4i0000-2-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ7844-4-4-4-44-24-44-22222-2−4i4i4i−4i0000-2-222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ798-88i−8i0008000-88i−8i0000000000000000000000000000000000000000000000000000000000000000000000
χ808-88i−8i000-40004−4i4i00000000000000000000002i6−2i626−2600000000000000000000000000000000000000000000
χ818-88i−8i000-40004−4i4i0000000000000000000000−2i62i6−262600000000000000000000000000000000000000000000
χ828-8−8i8i0008000-8−8i8i0000000000000000000000000000000000000000000000000000000000000000000000
χ838-8−8i8i000-400044i−4i00000000000000000000002i6−2i6−262600000000000000000000000000000000000000000000
χ848-8−8i8i000-400044i−4i0000000000000000000000−2i62i626−2600000000000000000000000000000000000000000000

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