Finite Group Databasebeta

← Group #10714569

Character table — Group #10714569

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order1222223444466666668888444488888812121212121212121212121224242424242424242424242424242424224466661212121216161616161616164488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ9222222222222222222-2-2-2-22222-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000
χ10222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222222222000000000000000000000000
χ11222222-12222-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ12222222-12222-1-1-1-1-1-1-122222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ13222222-12222-1-1-1-1-1-1-12222-2-2-2-222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-11111111122-2-2-1-1-1-11111000000000000
χ14222222-12222-1-1-1-1-1-1-12222-2-2-2-222-2-2-2-211111111-1-1-1-1-1-1-1-1-1-1-1-111111111-2-2221111-1-1-1-1000000000000
χ15222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000−i3−i3i3i3−i3−i3i3i3000000000000
χ16222222-12222-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000i3i3−i3−i3i3i3−i3−i3000000000000
χ17222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2222211111111-1-1-1-111111111-1-1-1-1-1-1-1-10000−i3−i3i3i3i3i3−i3−i3000000000000
χ18222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2222211111111-1-1-1-111111111-1-1-1-1-1-1-1-10000i3i3−i3−i3−i3−i3i3i3000000000000
χ192222-2-222-22-222-2-2-2-2222220000-2-20000000000002-22-22222-2-2-2-200000000000000000000000000002-200
χ202222-2-222-22-222-2-2-2-2222220000-2-20000000000002-22-22222-2-2-2-20000000000000000000000000000-2200
χ212222-2-222-22-222-2-2-2-22-2-2-2-20000220000000000002-22-2-2-2-2-222220000000000000000000000000000002i−2i
χ222222-2-222-22-222-2-2-2-22-2-2-2-20000220000000000002-22-2-2-2-2-22222000000000000000000000000000000−2i2i
χ232222-2-22-22-2222-2-2-2-22000000000022-2-200000000-22-22000000002222-2-2-2-200000000000022−2−222−2−20000
χ242222-2-22-22-2222-2-2-2-22000000000022-2-200000000-22-22000000002222-2-2-2-2000000000000−2−222−2−2220000
χ252222-2-22-22-2222-2-2-2-220000000000-2-22200000000-22-2200000000-2-2-2-2222200000000000022−2−2−2−2220000
χ262222-2-22-22-2222-2-2-2-220000000000-2-22200000000-22-2200000000-2-2-2-22222000000000000−2−22222−2−20000
χ2722-2-22-22-222-2-2-222-2-2222-2-200002-2000000000000-222-222-2-222-2-20000000000000000000000002i−2i2i−2i0000
χ2822-2-22-22-222-2-2-222-2-2222-2-200002-2000000000000-222-222-2-222-2-2000000000000000000000000−2i2i−2i2i0000
χ2922-2-22-22-222-2-2-222-2-22-2-2220000-22000000000000-222-2-2-222-2-222000000000000000000002i−2i2i−2i00000000
χ3022-2-22-22-222-2-2-222-2-22-2-2220000-22000000000000-222-2-2-222-2-22200000000000000000000−2i2i−2i2i00000000
χ3122-2-2-22222-2-2-2-2-2-2222000022-2-20000002222-2-2-2-222-2-20000000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ3222-2-2-22222-2-2-2-2-2-2222000022-2-20000002222-2-2-2-222-2-20000000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ3322-2-2-22222-2-2-2-2-2-22220000-2-222000000-2-2-2-2222222-2-20000000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ3422-2-2-22222-2-2-2-2-2-22220000-2-222000000-2-2-2-2222222-2-20000000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ3522-2-2-222-2-222-2-2-2-222222-2-20000-22000000000000-2-22222-2-2-2-22200000000002-200002-22-2000000000000
χ3622-2-2-222-2-222-2-2-2-222222-2-20000-22000000000000-2-22222-2-2-2-2220000000000-220000-22-22000000000000
χ3722-2-2-222-2-222-2-2-2-2222-2-22200002-2000000000000-2-222-2-22222-2-2000000002-2002-22-20000000000000000
χ3822-2-2-222-2-222-2-2-2-2222-2-22200002-2000000000000-2-222-2-22222-2-200000000-2200-22-220000000000000000
χ3922-2-2-22-1-2-2221111-1-1-122-2-20000-220000−i3−i3i3i3−i3−i3i3i311-1-1-1-11111-1-1−i3−i3i3i3−i3−i3i3i3002-2−i3i3i3−i3-11-11000000000000
χ4022-2-2-22-1-2-2221111-1-1-122-2-20000-220000−i3−i3i3i3−i3−i3i3i311-1-1-1-11111-1-1−i3−i3i3i3−i3−i3i3i300-22i3−i3−i3i31-11-1000000000000
χ4122-2-2-22-1-2-2221111-1-1-122-2-20000-220000i3i3−i3−i3i3i3−i3−i311-1-1-1-11111-1-1i3i3−i3−i3i3i3−i3−i3002-2i3−i3−i3i3-11-11000000000000
χ4222-2-2-22-1-2-2221111-1-1-122-2-20000-220000i3i3−i3−i3i3i3−i3−i311-1-1-1-11111-1-1i3i3−i3−i3i3i3−i3−i300-22−i3i3i3−i31-11-1000000000000
χ4322-2-2-22-1-2-2221111-1-1-1-2-22200002-20000−i3−i3i3i3−i3−i3i3i311-1-111-1-1-1-111i3i3−i3−i3i3i3−i3−i32-200-11-11−i3i3i3−i3000000000000
χ4422-2-2-22-1-2-2221111-1-1-1-2-22200002-20000−i3−i3i3i3−i3−i3i3i311-1-111-1-1-1-111i3i3−i3−i3i3i3−i3−i3-22001-11-1i3−i3−i3i3000000000000
χ4522-2-2-22-1-2-2221111-1-1-1-2-22200002-20000i3i3−i3−i3i3i3−i3−i311-1-111-1-1-1-111−i3−i3i3i3−i3−i3i3i32-200-11-11i3−i3−i3i3000000000000
χ4622-2-2-22-1-2-2221111-1-1-1-2-22200002-20000i3i3−i3−i3i3i3−i3−i311-1-111-1-1-1-111−i3−i3i3i3−i3−i3i3i3-22001-11-1−i3i3i3−i3000000000000
χ474444444-4-4-4-444444440000000000000000000000-4-4-4-40000000000000000000000000000000000000000
χ48444444-2-4-4-4-4-2-2-2-2-2-2-200000000000000−2i3−2i32i32i32i32i3−2i3−2i322220000000000000000000000000000000000000000
χ49444444-2-4-4-4-4-2-2-2-2-2-2-2000000000000002i32i3−2i3−2i3−2i3−2i32i32i322220000000000000000000000000000000000000000
χ504444-4-4-24-44-4-2-22222-244440000-4-4000000000000-22-22-2-2-2-2222200000000000000000000000000000000
χ514444-4-4-24-44-4-2-22222-2-4-4-4-4000044000000000000-22-222222-2-2-2-200000000000000000000000000000000
χ524444-4-4-2-44-44-2-22222-2000000000044-4-4000000002-22-200000000-2-2-2-22222000000000000000000000000
χ534444-4-4-2-44-44-2-22222-20000000000-4-444000000002-22-2000000002222-2-2-2-2000000000000000000000000
χ5444-4-44-444-4-44-4-444-4-4400000000000000000000004-4-440000000000000000000000000000000000000000
χ5544-4-44-4-24-4-4422-2-222-20000000000000000000000-222-200000000−2i3−2i32i32i32i32i3−2i3−2i3000000000000000000000000
χ5644-4-44-4-24-4-4422-2-222-20000000000000000000000-222-2000000002i32i3−2i3−2i3−2i3−2i32i32i3000000000000000000000000
χ5744-4-44-4-2-444-422-2-222-244-4-400004-40000000000002-2-22-2-222-2-22200000000000000000000000000000000
χ5844-4-44-4-2-444-422-2-222-2-4-4440000-440000000000002-2-2222-2-222-2-200000000000000000000000000000000
χ5944-4-4-44-244-4-42222-2-2-2000044-4-4000000-2-2-2-22222-2-2220000000000000000000000000000000000000000
χ6044-4-4-44-244-4-42222-2-2-20000-4-4440000002222-2-2-2-2-2-2220000000000000000000000000000000000000000
χ614-44-400400004-40000-422−2222−222i−2i2i−2i0000−2i22i22i−2i2i−2i2i−2i2i−2i000022−2222−2200000000−2i22i2−2i22i2000000000000000000000000
χ624-44-400400004-40000-422−2222−22−2i2i−2i2i00002i2−2i2−2i2i−2i2i−2i2i−2i2i000022−2222−22000000002i2−2i22i2−2i2000000000000000000000000
χ634-44-400400004-40000-4−2222−22222i−2i2i−2i00002i2−2i22i−2i2i−2i2i−2i2i−2i0000−2222−2222000000002i2−2i22i2−2i2000000000000000000000000
χ644-44-400400004-40000-4−2222−2222−2i2i−2i2i0000−2i22i2−2i2i−2i2i−2i2i−2i2i0000−2222−222200000000−2i22i2−2i22i2000000000000000000000000
χ654-44-400-20000-22−2i32i3−2i32i3222−2222−222i−2i2i−2i0000−2i22i22ζ14−2ζ142ζ22−2ζ222ζ22−2ζ222ζ14−2ζ140000−22−22i6−i6i6−i66−66−6i2−i2i2−i2000000000000000000000000
χ664-44-400-20000-22−2i32i3−2i32i3222−2222−22−2i2i−2i2i00002i2−2i2−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22−2ζ142ζ140000−22−22i6−i6i6−i6−66−66−i2i2−i2i2000000000000000000000000
χ674-44-400-20000-22−2i32i3−2i32i32−2222−22222i−2i2i−2i00002i2−2i22ζ14−2ζ142ζ22−2ζ222ζ22−2ζ222ζ14−2ζ1400002−22−2−i6i6−i6i6−66−66−i2i2−i2i2000000000000000000000000
χ684-44-400-20000-22−2i32i3−2i32i32−2222−2222−2i2i−2i2i0000−2i22i2−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22−2ζ142ζ1400002−22−2−i6i6−i6i66−66−6i2−i2i2−i2000000000000000000000000
χ694-44-400-20000-222i3−2i32i3−2i3222−2222−222i−2i2i−2i0000−2i22i22ζ22−2ζ222ζ14−2ζ142ζ14−2ζ142ζ22−2ζ220000−22−22−i6i6−i6i6−66−66i2−i2i2−i2000000000000000000000000
χ704-44-400-20000-222i3−2i32i3−2i3222−2222−22−2i2i−2i2i00002i2−2i2−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14−2ζ222ζ220000−22−22−i6i6−i6i66−66−6−i2i2−i2i2000000000000000000000000
χ714-44-400-20000-222i3−2i32i3−2i32−2222−22222i−2i2i−2i00002i2−2i22ζ22−2ζ222ζ14−2ζ142ζ14−2ζ142ζ22−2ζ2200002−22−2i6−i6i6−i66−66−6−i2i2−i2i2000000000000000000000000
χ724-44-400-20000-222i3−2i32i3−2i32−2222−2222−2i2i−2i2i0000−2i22i2−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14−2ζ222ζ2200002−22−2i6−i6i6−i6−66−66i2−i2i2−i2000000000000000000000000
χ734-4-440040000-440000-422−22−22222i−2i−2i2i00−2i22i2002i−2i2i−2i−2i2i−2i2i000022−22−22220000−2i22i22i2−2i20000000000000000000000000000
χ744-4-440040000-440000-422−22−2222−2i2i2i−2i002i2−2i200−2i2i−2i2i2i−2i2i−2i000022−22−222200002i2−2i2−2i22i20000000000000000000000000000
χ754-4-440040000-440000-4−222222−222i−2i−2i2i002i2−2i2002i−2i2i−2i−2i2i−2i2i0000−222222−2200002i2−2i2−2i22i20000000000000000000000000000
χ764-4-440040000-440000-4−222222−22−2i2i2i−2i00−2i22i200−2i2i−2i2i2i−2i2i−2i0000−222222−220000−2i22i22i2−2i20000000000000000000000000000
χ774-4-4400-200002-2−2i32i32i3−2i3222−22−22222i−2i−2i2i00−2i22i2002ζ22−2ζ222ζ14−2ζ14−2ζ142ζ14−2ζ222ζ220000−222−2i6−i6−i6i6i2−i2−i2i2−666−6000000000000000000000000
χ784-4-4400-200002-2−2i32i32i3−2i3222−22−2222−2i2i2i−2i002i2−2i200−2ζ222ζ22−2ζ142ζ142ζ14−2ζ142ζ22−2ζ220000−222−2i6−i6−i6i6−i2i2i2−i26−6−66000000000000000000000000
χ794-4-4400-200002-2−2i32i32i3−2i32−222222−222i−2i−2i2i002i2−2i2002ζ22−2ζ222ζ14−2ζ14−2ζ142ζ14−2ζ222ζ2200002−2−22−i6i6i6−i6−i2i2i2−i26−6−66000000000000000000000000
χ804-4-4400-200002-2−2i32i32i3−2i32−222222−22−2i2i2i−2i00−2i22i200−2ζ222ζ22−2ζ142ζ142ζ14−2ζ142ζ22−2ζ2200002−2−22−i6i6i6−i6i2−i2−i2i2−666−6000000000000000000000000
χ814-4-4400-200002-22i3−2i3−2i32i3222−22−22222i−2i−2i2i00−2i22i2002ζ14−2ζ142ζ22−2ζ22−2ζ222ζ22−2ζ142ζ140000−222−2−i6i6i6−i6i2−i2−i2i26−6−66000000000000000000000000
χ824-4-4400-200002-22i3−2i3−2i32i3222−22−2222−2i2i2i−2i002i2−2i200−2ζ142ζ14−2ζ222ζ222ζ22−2ζ222ζ14−2ζ140000−222−2−i6i6i6−i6−i2i2i2−i2−666−6000000000000000000000000
χ834-4-4400-200002-22i3−2i3−2i32i32−222222−222i−2i−2i2i002i2−2i2002ζ14−2ζ142ζ22−2ζ22−2ζ222ζ22−2ζ142ζ1400002−2−22i6−i6−i6i6−i2i2i2−i2−666−6000000000000000000000000
χ844-4-4400-200002-22i3−2i3−2i32i32−222222−22−2i2i2i−2i00−2i22i200−2ζ142ζ14−2ζ222ζ222ζ22−2ζ222ζ14−2ζ1400002−2−22i6−i6−i6i6i2−i2−i2i26−6−66000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.