Finite Group Databasebeta

← Group #10778214

Character table — Group #10778214

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222244444444444444466668888888888888888881212121216161616161624242424242424242432324848
order12223444466644444881212121224242424444488888881212121212242424242424248822242424242488888886644
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-111-1-1111-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111-1-1-1-1111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111
χ511111111111111111-1-11111-1-1-1-11111-1-1-111-1-111111-1-1-1-1-1-111-1-11-111-1-11111-1-1-1-1-11-11-1
χ611111111111111111-1-11111-1-1-1-11111-1-1-1-1-11111111-1-1-1-1-1-111-1-1-11-1-11111-1-1-1-1-111-11-11
χ711111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1111111-1-11
χ811111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-111-11-1-111-1-111111-1-1-111-1
χ91111111111111-1-1-1-1111111111111111-1-111111-1-1-1-111-1-1-1-11111-1-11111-1-1111-1-111-1-1-1-1
χ101111111111111-1-1-1-1111111111111111-1-1-1-1-1-11-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-11111
χ111111111111111-1-1-1-11111111111-1-1-1-11-1-111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1-1-111
χ121111111111111-1-1-1-11111111111-1-1-1-11-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1111111-1-1
χ131111111111111-1-1-1-1-1-11111-1-1-1-11111-11111-1-11-1-1-1-1-1-1111111-1-1-1111-1-1-1-111-111-1-1-11-11
χ141111111111111-1-1-1-1-1-11111-1-1-1-11111-111-1-1111-1-1-1-1-1-1111111-1-11-1-1-111-1-1-1-1-111111-11-1
χ151111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-11111-1-111-1111-1-111-1-11-1-111-111-1
χ161111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-1-11111-1-1111-1-1-11111111-1-1-1-11-1-11
χ17222222-22-2222-2000022-222-222222222-2000000-20000-2-20000-2-2220000000000-200000000
χ18222222-22-2222-2000022-222-22222-2-2-2-2-2000000-20000-2-2000022-2-20000000000200000000
χ19222222-22-2222-20000-2-2-222-2-2-2-2-222222000000-20000220000-2-2-2-20000000000200000000
χ20222222-22-2222-20000-2-2-222-2-2-2-2-2-2-2-2-22000000-2000022000022220000000000-200000000
χ2122222-22-22222-222-2-2002-2-22000022-2-20000000-222-2-20000002-2000000002-200000000000
χ2222222-22-22222-222-2-2002-2-220000-2-2220000000-222-2-2000000-2200000000-2200000000000
χ2322222-22-22222-2-2-222002-2-22000022-2-20000000-2-2-2220000002-200000000-2200000000000
χ2422222-22-22222-2-2-222002-2-220000-2-2220000000-2-2-222000000-22000000002-200000000000
χ2522222-2-2-2-22222000000-2-2-2-2000022-2-202i−2i000020000002i2i−2i−2i-2200000000000002i−2i000000
χ2622222-2-2-2-22222000000-2-2-2-2000022-2-20−2i2i00002000000−2i−2i2i2i-220000000000000−2i2i000000
χ2722222-2-2-2-22222000000-2-2-2-20000-2-22202i−2i000020000002i2i−2i−2i2-20000000000000−2i2i000000
χ2822222-2-2-2-22222000000-2-2-2-20000-2-2220−2i2i00002000000−2i−2i2i2i2-200000000000002i−2i000000
χ292222-12222-1-1-12222222-1-1-1-1-1-1-1-100002222222-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1000000000-1-100
χ302222-12222-1-1-12222222-1-1-1-1-1-1-1-10000222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-10000-2-211110000000001100
χ312222-12222-1-1-122222-2-2-1-1-1-111110000-2-2-222-2-2-1-1-1-1-111111100002-2-1-111000000000-1100
χ322222-12222-1-1-122222-2-2-1-1-1-111110000-2-2-2-2-222-1-1-1-1-11111110000-2211-1-10000000001-100
χ332222-12222-1-1-12-2-2-2-222-1-1-1-1-1-1-1-100002-2-22222-11111-1-111110000-2-2-1-1-1-10000000001100
χ342222-12222-1-1-12-2-2-2-222-1-1-1-1-1-1-1-100002-2-2-2-2-2-2-11111-1-111110000221111000000000-1-100
χ352222-12222-1-1-12-2-2-2-2-2-2-1-1-1-111110000-22222-2-2-1111111-1-1-1-10000-22-1-1110000000001-100
χ362222-12222-1-1-12-2-2-2-2-2-2-1-1-1-111110000-222-2-222-1111111-1-1-1-100002-211-1-1000000000-1100
χ3722-2-22-20202-2-2000002-202-2022-2-22i−2i2i−2i000−i2i2−i2i200000000000002i−2i00−i2i2−i2i2002−20002−20000
χ3822-2-22-20202-2-2000002-202-2022-2-22i−2i2i−2i000i2−i2i2−i200000000000002i−2i00i2−i2i2−i200−22000−220000
χ3922-2-22-20202-2-2000002-202-2022-2-2−2i2i−2i2i000−i2i2−i2i20000000000000−2i2i00−i2i2−i2i200−22000−220000
χ4022-2-22-20202-2-2000002-202-2022-2-2−2i2i−2i2i000i2−i2i2−i20000000000000−2i2i00i2−i2i2−i2002−20002−20000
χ4122-2-22-20202-2-200000-2202-20-2-2222i−2i2i−2i000−i2i2i2−i20000000000000−2i2i00−i2i2i2−i2002−2000−220000
χ4222-2-22-20202-2-200000-2202-20-2-2222i−2i2i−2i000i2−i2−i2i20000000000000−2i2i00i2−i2−i2i200−220002−20000
χ4322-2-22-20202-2-200000-2202-20-2-222−2i2i−2i2i000−i2i2i2−i200000000000002i−2i00−i2i2i2−i200−220002−20000
χ4422-2-22-20202-2-200000-2202-20-2-222−2i2i−2i2i000i2−i2−i2i200000000000002i−2i00i2−i2−i2i2002−2000−220000
χ454444-24-44-4-2-2-2-40000442-2-22-2-2-2-20000-40000002000022000000000000000000000000000
χ464444-24-44-4-2-2-2-40000-4-42-2-2222220000400000020000-2-2000000000000000000000000000
χ474444-2-44-44-2-2-2-444-4-400-222-20000000000000002-2-22200000000000000000000000000000
χ484444-2-44-44-2-2-2-4-4-44400-222-2000000000000000222-2-200000000000000000000000000000
χ494444-2-4-4-4-4-2-2-2400000022220000000004i−4i0000-2000000−2i−2i2i2i00000000000000000000000
χ504444-2-4-4-4-4-2-2-240000002222000000000−4i4i0000-20000002i2i−2i−2i00000000000000000000000
χ5144-4-4440-404-4-400000000-44000004i−4i−4i4i00000000000000000000000000000000000000000
χ5244-4-4440-404-4-400000000-4400000−4i4i4i−4i00000000000000000000000000000000000000000
χ5344-4-4-2-4040-222000004-40-220-2-2220000000−2i22i2−2i22i200000000000000000i2−i2i2−i20000000000000
χ5444-4-4-2-4040-222000004-40-220-2-22200000002i2−2i22i2−2i200000000000000000−i2i2−i2i20000000000000
χ5544-4-4-2-4040-22200000-440-22022-2-20000000−2i22i22i2−2i200000000000000000i2−i2−i2i20000000000000
χ5644-4-4-2-4040-22200000-440-22022-2-200000002i2−2i2−2i22i200000000000000000−i2i2i2−i20000000000000
χ574-44-44040-4-44-40004i−4i00400-40000000000000000004i−4i00000000000000000000000000000
χ584-44-44040-4-44-4000−4i4i00400-4000000000000000000−4i4i00000000000000000000000000000
χ594-44-440-404-44-404-40000-400400000000000000004-40000000000000000000000000000000
χ604-44-440-404-44-40-440000-40040000000000000000-440000000000000000000000000000000
χ614-44-4-2040-42-220004i−4i00-2002i6−i6i6−i600000000000000−2i2ii6−i66−66−600000000000000000000000
χ624-44-4-2040-42-220004i−4i00-2002−i6i6−i6i600000000000000−2i2i−i6i6−66−6600000000000000000000000
χ634-44-4-2040-42-22000−4i4i00-2002i6−i6i6−i6000000000000002i−2ii6−i6−66−6600000000000000000000000
χ644-44-4-2040-42-22000−4i4i00-2002−i6i6−i6i6000000000000002i−2i−i6i66−66−600000000000000000000000
χ654-44-4-20-4042-2204-40000200-2i6−i6i6−i6000000000000-2200−i6i6i6−i6−i6i600000000000000000000000
χ664-44-4-20-4042-2204-40000200-2−i6i6−i6i6000000000000-2200i6−i6−i6i6i6−i600000000000000000000000
χ674-44-4-20-4042-220-440000200-2i6−i6i6−i60000000000002-200−i6i6−i6i6i6−i600000000000000000000000
χ684-44-4-20-4042-220-440000200-2−i6i6−i6i60000000000002-200i6−i6i6−i6−i6i600000000000000000000000
χ6988-8-8-480-80-444000000004-400000000000000000000000000000000000000000000000000
χ708-8-8880000-8-88000000000000000000000000000000000000000000000000000000000000
χ718-8-88-4000044-4000000000002i6−2i6−2i62i6000000000000000000000000000000000000000000000
χ728-8-88-4000044-400000000000−2i62i62i6−2i6000000000000000000000000000000000000000000000

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