Finite Group Databasebeta

← Group #10858709

Character table — Group #10858709

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size1111222222222244444444888888888888812121212121212121212161616161616161616161616161624242424242424242448
order12222234444666668812121212444444888242424242244444488881212121212122424242424244444448884
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-111-11-1-1111111111111-1-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-111-1-1
χ4111111111111111111111111-111-11-1-11111-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111-1-11-1-111-1-111111111-1-1-1-1-1-11-11-1-1-1-1111-1-1-1-11111-1-1-1-1-11
χ61111111111111111111111-1-11-1-111-1-11111-1-1-1-11111111-11-1-1-1-1111-1-1-1-1-1-1-1-111111-1
χ71111111111111111111111-1-1-1-1-1-111111111111-1-1-1-111-11-1-1-1-1-1-1-1-1111111-1-111-1-11-1
χ81111111111111111111111-1-1-1-1-1-11111111-1-1-1-11111-1-1-11-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ91111111111111111-1-11111111-1-11-1-1-1-1-1-1-11111-1-1-1-1-1-1-11111-1-11-1-111-1-1-1-1111111-1-1
χ101111111111111111-1-11111111-1-11-1-1-1-1-1-1-1-1-1-1-1111111-11111-1-11-1-111-1-111-1-1-1-1-1-111
χ111111111111111111-1-1111111-1-1-1-1-111-1-1-1-11111-1-1-1-1111-1-111-1-1-111-1-111-1-1-1-1-1-11111
χ121111111111111111-1-1111111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-11-1-111-1-1-111-1-111111111-1-1-1-1
χ131111111111111111-1-11111-1-11111-111-1-1-1-11111111111-1-11-1-1111-1-1-1-111-1-111-1-1-1-11-1
χ141111111111111111-1-11111-1-11111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-11111-1-11111-11
χ151111111111111111-1-11111-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-111-11111-1-1-1-1-1-111-1-1-11
χ161111111111111111-1-11111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-11111-1-11111-1-1111-1
χ17222222-12222-1-1-1-1-122-1-1-1-1222222222-1-1-1-1000000000022-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ18222222-12222-1-1-1-1-122-1-1-1-122-222-22-2-2-1-1-1-10000000000-2-21-1-1-1-111111110000000000
χ19222222-12222-1-1-1-1-122-1-1-1-1-2-22-2-222-2-2-1-1-1-100000000002-2-11111-1-1-111110000000000
χ20222222-12222-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2222-1-1-1-10000000000-2211111111-1-1-1-10000000000
χ21222222-12222-1-1-1-1-1-2-2-1-1-1-1222-2-22-2-2-211110000000000-22-1-1-111-111-1-1110000000000
χ22222222-12222-1-1-1-1-1-2-2-1-1-1-122-2-2-2-2-222111100000000002-21-1-1111-1-111-1-10000000000
χ23222222-12222-1-1-1-1-1-2-2-1-1-1-1-2-22222-22211110000000000-2-2-111-1-1-11111-1-10000000000
χ24222222-12222-1-1-1-1-1-2-2-1-1-1-1-2-2-222-2-2-2-21111000000000022111-1-11-1-1-1-1110000000000
χ252222-2-222-2-22222-2-2002-22-200200-20000000000022-2-2220020000-200000000000000-20
χ262222-2-222-2-22222-2-2002-22-200200-200000000000-2-222-2-20020000-20000000000000020
χ272222-2-222-2-22222-2-2002-22-200-20020000000000022-2-2-2-200-2000020000000000000020
χ282222-2-222-2-22222-2-2002-22-200-200200000000000-2-2222200-20000200000000000000-20
χ292222-2-22-222-2222-2-222-22-22000000-20022-2-222-2-2000000000000000000002-200000000
χ302222-2-22-222-2222-2-222-22-22000000-20022-2-2-2-22200000000000000000000-2200000000
χ312222-2-22-222-2222-2-2-2-2-22-22000000200-2-22222-2-200000000000000000000-2200000000
χ322222-2-22-222-2222-2-2-2-2-22-22000000200-2-222-2-222000000000000000000002-200000000
χ3322-2-22-222-22-2-22-22-20022-2-22-2000000000002-22-20000000002-20000000000000002-200
χ3422-2-22-222-22-2-22-22-20022-2-22-200000000000-22-220000000002-2000000000000000-2200
χ3522-2-22-222-22-2-22-22-20022-2-2-22000000000002-22-2000000000-22000000000000000-2200
χ3622-2-22-222-22-2-22-22-20022-2-2-2200000000000-22-22000000000-220000000000000002-200
χ3722-2-22-22-22-22-22-22-200-2-22200000002-2000000002i−2i2i−2i000000000000002-2002i−2i000000
χ3822-2-22-22-22-22-22-22-200-2-22200000002-200000000−2i2i−2i2i000000000000002-200−2i2i000000
χ3922-2-22-22-22-22-22-22-200-2-2220000000-22000000002i−2i2i−2i00000000000000-2200−2i2i000000
χ4022-2-22-22-22-22-22-22-200-2-2220000000-2200000000−2i2i−2i2i00000000000000-22002i−2i000000
χ4122-2-2-222-2-222-22-2-2200-222-20002i−2i000000002-2-222i−2i−2i2i00000002i−2i00000000000000000
χ4222-2-2-222-2-222-22-2-2200-222-20002i−2i00000000-222-2−2i2i2i−2i00000002i−2i00000000000000000
χ4322-2-2-222-2-222-22-2-2200-222-2000−2i2i000000002-2-22−2i2i2i−2i0000000−2i2i00000000000000000
χ4422-2-2-222-2-222-22-2-2200-222-2000−2i2i00000000-222-22i−2i−2i2i0000000−2i2i00000000000000000
χ454444444-4-4-4-44444400-4-4-4-400000000000000000000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-2-2-2002222000000000000000000000000000000023−2300000000000000
χ47444444-2-4-4-4-4-2-2-2-2-20022220000000000000000000000000000000−232300000000000000
χ484444-4-4-24-4-44-2-2-22200-22-2200400-40000000000000000000-2000020000000000000000
χ494444-4-4-24-4-44-2-2-22200-22-2200-4004000000000000000000020000-20000000000000000
χ504444-4-4-2-444-4-2-2-222442-22-2000000-400-2-2220000000000000000000000000000000000
χ514444-4-4-2-444-4-2-2-222-4-42-22-200000040022-2-20000000000000000000000000000000000
χ5244-4-44-4-24-44-42-22-2200-2-2224-4000000000000000000000000-220000000000000000000
χ5344-4-44-4-24-44-42-22-2200-2-222-440000000000000000000000002-20000000000000000000
χ5444-4-44-4-2-44-442-22-220022-2-200000004-400000000000000000000000000-220000000000
χ5544-4-44-4-2-44-442-22-220022-2-20000000-44000000000000000000000000002-20000000000
χ5644-4-4-44444-4-4-44-4-44004-4-4400000000000000000000000000000000000000000000000
χ5744-4-4-44-244-4-42-222-200-222-200000000000000000000000000000000023−23000000000000
χ5844-4-4-44-244-4-42-222-200-222-2000000000000000000000000000000000−2323000000000000
χ5944-4-4-44-2-4-4442-222-2002-2-220004i−4i00000000000000000000000−2i2i00000000000000000
χ6044-4-4-44-2-4-4442-222-2002-2-22000−4i4i000000000000000000000002i−2i00000000000000000
χ614-44-400400004-4-40022−22000000000000022−22000000000022−220000000000000000002-20000
χ624-44-400400004-4-40022−22000000000000022−220000000000−2222000000000000000000-220000
χ634-44-400400004-4-400−22220000000000000−2222000000000022−22000000000000000000-220000
χ644-44-400400004-4-400−22220000000000000−22220000000000−22220000000000000000002-20000
χ658-88-800-40000-4440042−420000000000000−2222000000000000000000000000000000000000
χ668-88-800-40000-44400−4242000000000000022−22000000000000000000000000000000000000
χ678-8-880080000-8-880000000000000000000000000000000000000000000000000000000
χ688-8-8800-4000044-4000000000000000000026−260000000000000000000000000000000000
χ698-8-8800-4000044-40000000000000000000−26260000000000000000000000000000000000

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