Finite Group Databasebeta

← Group #10714581

Character table — Group #10714581

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222222222444444448888888888888888161616161616161616161616242424242424242448484848
order124422234446661212121266888812124488121212122424242424242424224466661212121216161616161616164488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-111-1-111-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-111-1-111-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-111-1-1111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-1-1-1-1111111-1-1
χ922222222222222222222-2-2-2-22222-2-22222-2-2-2-2-2-2-2-2000000000000000000000000
χ1022222222222222222222-2-2-2-222-2-222-2-2-2-2-2-2-2-22222000000000000000000000000
χ112222222-1222-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ122222222-1222-1-1-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ132222222-1222-1-1-1-1-1-1-1-1-12222-1-1-2-2-2-21111-1-1-1-111112-22-2-1-111-1-111000000000000
χ142222222-1222-1-1-1-1-1-1-1-1-12222-1-1-2-2-2-21111-1-1-1-11111-22-2211-1-111-1-1000000000000
χ152222222-1222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-122-2-2-1-1-1-1111111110000−i3i3−i3i3−i3i3−i3i3000000000000
χ162222222-1222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-122-2-2-1-1-1-1111111110000i3−i3i3−i3i3−i3i3−i3000000000000
χ172222222-1222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-2-22211111111-1-1-1-10000−i3i3i3−i3−i3i3i3−i3000000000000
χ182222222-1222-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-2-22211111111-1-1-1-10000i3−i3−i3i3i3−i3−i3i3000000000000
χ1922222-2-22-22-2-2-2222-2-22-22-22-22-20000000022-2-2000000000000000000002i2i−2i−2i0000
χ2022222-2-22-22-2-2-2222-2-22-22-22-22-20000000022-2-200000000000000000000−2i−2i2i2i0000
χ2122222-2-22-22-2-2-2222-2-22-2-22-222-200000000-2-22200000000000000002i2i−2i−2i00000000
χ2222222-2-22-22-2-2-2222-2-22-2-22-222-200000000-2-2220000000000000000−2i−2i2i2i00000000
χ232222-22-222-2-22222222-2-20000-2-22-20022-2-200000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ242222-22-222-2-22222222-2-20000-2-22-20022-2-200000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ252222-22-222-2-22222222-2-20000-2-2-2200-2-22200000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ262222-22-222-2-22222222-2-20000-2-2-2200-2-22200000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ272222-2-222-2-22-2-2222-2-2-220000-22002-20000000022-2-20000000000002−2−222−2−220000
χ282222-2-222-2-22-2-2222-2-2-220000-22002-20000000022-2-2000000000000−222−2−222−20000
χ292222-2-222-2-22-2-2222-2-2-220000-2200-2200000000-2-2220000000000002−2−22−222−20000
χ302222-2-222-2-22-2-2222-2-2-220000-2200-2200000000-2-222000000000000−222−22−2−220000
χ3122-2-2-22-22-222222-2-2-2-2-2-22-2-2222000000002-22-2000020-202200-2-200000000000000
χ3222-2-2-22-22-222222-2-2-2-2-2-22-2-2222000000002-22-20000-2020-2-2002200000000000000
χ3322-2-2-22-22-222222-2-2-2-2-2-2-222-22200000000-22-220000020-2002200-2-2000000000000
χ3422-2-2-22-22-222222-2-2-2-2-2-2-222-22200000000-22-2200000-20200-2-20022000000000000
χ3522-2-2-22-2-1-222-1-1-11111112-2-22-1-10000−i3i3−i3i3-11-11−i3i3−i3i320-20-1-1−i3i311i3−i3000000000000
χ3622-2-2-22-2-1-222-1-1-11111112-2-22-1-10000−i3i3−i3i3-11-11−i3i3−i3i3-202011i3−i3-1-1−i3i3000000000000
χ3722-2-2-22-2-1-222-1-1-11111112-2-22-1-10000i3−i3i3−i3-11-11i3−i3i3−i320-20-1-1i3−i311−i3i3000000000000
χ3822-2-2-22-2-1-222-1-1-11111112-2-22-1-10000i3−i3i3−i3-11-11i3−i3i3−i3-202011−i3i3-1-1i3−i3000000000000
χ3922-2-2-22-2-1-222-1-1-1111111-222-2-1-10000−i3i3−i3i31-11-1i3−i3i3−i3020-2−i3i3-1-1i3−i311000000000000
χ4022-2-2-22-2-1-222-1-1-1111111-222-2-1-10000−i3i3−i3i31-11-1i3−i3i3−i30-202i3−i311−i3i3-1-1000000000000
χ4122-2-2-22-2-1-222-1-1-1111111-222-2-1-10000i3−i3i3−i31-11-1−i3i3−i3i3020-2i3−i3-1-1−i3i311000000000000
χ4222-2-2-22-2-1-222-1-1-1111111-222-2-1-10000i3−i3i3−i31-11-1−i3i3−i3i30-202−i3i311i3−i3-1-1000000000000
χ4322-2-2-2-22222-2-2-22-2-222-2222-2-22-2000000002-2-22000000000000000000000000002i−2i
χ4422-2-2-2-22222-2-2-22-2-222-2222-2-22-2000000002-2-2200000000000000000000000000−2i2i
χ4522-2-2-2-22222-2-2-22-2-222-22-2-2222-200000000-222-20000000000000000000000002-200
χ4622-2-2-2-22222-2-2-22-2-222-22-2-2222-200000000-222-2000000000000000000000000-2200
χ4744444-4-4-2-44-422-2-2-222-224-44-4-2200000000-2-2220000000000000000000000000000
χ4844444-4-4-2-44-422-2-2-222-22-44-44-220000000022-2-20000000000000000000000000000
χ494444-44-4-24-4-4-2-2-2-2-2-2-2220000224-400-2-22200000000000000000000000000000000
χ504444-44-4-24-4-4-2-2-2-2-2-2-222000022-440022-2-200000000000000000000000000000000
χ514444-4-44-2-4-4422-2-2-2222-200002-2004-400000000-2-222000000000000000000000000
χ524444-4-44-2-4-4422-2-2-2222-200002-200-440000000022-2-2000000000000000000000000
χ5344-4-44444-4-4-4444-4-4-4-4440000-4-40000000000000000000000000000000000000000
χ5444-4-4444-2-4-4-4-2-2-22222-2-20000220000−2i32i32i3−2i300000000000000000000000000000000
χ5544-4-4444-2-4-4-4-2-2-22222-2-200002200002i3−2i3−2i32i300000000000000000000000000000000
χ5644-4-44-4-444-44-4-44-4-4444-40000-440000000000000000000000000000000000000000
χ5744-4-44-4-4-24-4422-222-2-2-2200002-2000000000000−2i32i32i3−2i3000000000000000000000000
χ5844-4-44-4-4-24-4422-222-2-2-2200002-20000000000002i3−2i3−2i32i3000000000000000000000000
χ5944-4-4-4-44-244-422-222-2-22-244-4-4-2200000000-222-20000000000000000000000000000
χ6044-4-4-4-44-244-422-222-2-22-2-4-444-22000000002-2-220000000000000000000000000000
χ618-88i−8i000800000-88i−8i00000000000000000000000000000000000000000000000000
χ628-88i−8i000-4000−4i34i34−4i4i43−43000000000000000000000000000000000000000000000000
χ638-88i−8i000-40004i3−4i34−4i4i−4343000000000000000000000000000000000000000000000000
χ648-8−8i8i000800000-8−8i8i00000000000000000000000000000000000000000000000000
χ658-8−8i8i000-4000−4i34i344i−4i−4343000000000000000000000000000000000000000000000000
χ668-8−8i8i000-40004i3−4i344i−4i43−43000000000000000000000000000000000000000000000000

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