Finite Group Databasebeta

← Group #10836672

Character table — Group #10836672

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222444444446688888888888881212121212121212121616161616161616161616161616242424242424244848
order1222223444466666881212121244244488888242424244444444884681212121212242424242424448888848
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-11111111111111111-11-11-1-1-1-111-1-1-1-1-1-1111-1-1-1-1
χ3111111111111111111111111-1-111-1-11-1-1111111-1-11-1-1111-1-1-11111-1-1-1-1-1-1111-1-1-1-11-1
χ4111111111111111111111111-1-1-1-1111-1-1111111-1-11-1-111-1-11-1-1-1-1-1-1-11111-1-11-1-111-11
χ51111111111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-1-1-111-1-1-11111
χ71111111111111111111111-1-1-1-111-1-11-1-11111-1-111-111-1-11-1-1-11111-1-1-1-1-1-1-1-1-11111-11
χ81111111111111111111111-1-1-1-1-1-1111-1-11111-1-111-111-1-1-1-11-1-1-1-1-1-1-1111111-111-1-11-1
χ91111111111111111-1-1111111111111-1-1-1-1-1-1-11111111-1-1-11-1111-1-1-1-111-1-111-1-1-111-1-1
χ101111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-11111111-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-111
χ111111111111111111-1-1111111-1-111-1-1-111-1-1-1-111-1-11-1-1-1-1-1-11-111-1-111-1-11111-111-1-1-11
χ121111111111111111-1-1111111-1-1-1-111-111-1-1-1-111-1-11-1-1-1-11-1-1-1-1-1111111-1-1-1-1-111111-1
χ131111111111111111-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1111-1-1-1-111-1-1-1-1111-1-111
χ141111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1111111111-1-1
χ151111111111111111-1-11111-1-1-1-111-1-1-111-1-1-1-1-1-111-11111-1-11-111-1-111-1-111-1-11-1-1111-1
χ161111111111111111-1-11111-1-1-1-1-1-111-111-1-1-1-1-1-111-111111-1-1-1-1-1111111-1-1111-1-1-1-1-11
χ172222222-2-2-2-22222200-2-2-2-22200000002i−2i0000-2-20020000000000002i−2i00000002i−2i0000
χ182222222-2-2-2-22222200-2-2-2-2220000000−2i2i0000-2-2002000000000000−2i2i0000000−2i2i0000
χ192222222-2-2-2-22222200-2-2-2-2-2-200000002i−2i00002200-20000000000002i−2i0000000−2i2i0000
χ202222222-2-2-2-22222200-2-2-2-2-2-20000000−2i2i00002200-2000000000000−2i2i00000002i−2i0000
χ21222222-12222-1-1-1-1-122-1-1-1-100222222222-1-1-1-10000000002-12-1-1-1-1-1-1-1-1-1-1-1000000000
χ22222222-12222-1-1-1-1-122-1-1-1-10022-2-2-2-2222-1-1-1-1000000000-2-1-2-11111-1-11111000000000
χ23222222-12222-1-1-1-1-122-1-1-1-100-2-222-2-22-2-2-1-1-1-100000000021-21-1-1-1-1111111000000000
χ24222222-12222-1-1-1-1-122-1-1-1-100-2-2-2-2222-2-2-1-1-1-1000000000-2121111111-1-1-1-1000000000
χ25222222-12222-1-1-1-1-1-2-2-1-1-1-100222222-2-2-21111000000000-2-1-2-1-1-11111-1-111000000000
χ26222222-12222-1-1-1-1-1-2-2-1-1-1-10022-2-2-2-2-2-2-211110000000002-12-111-1-11111-1-1000000000
χ27222222-12222-1-1-1-1-1-2-2-1-1-1-100-2-222-2-2-2221111000000000-2121-1-111-1-111-1-1000000000
χ28222222-12222-1-1-1-1-1-2-2-1-1-1-100-2-2-2-222-222111100000000021-2111-1-1-1-1-1-111000000000
χ292222-2-222-2-22222-2-20022-2-2222-2000000000002-2-2-2-22200020-20000000000000000000
χ302222-2-222-2-22222-2-20022-2-222-22000000000002-222-2-2-2000-2020000000000000000000
χ312222-2-222-2-22222-2-20022-2-2-2-22-200000000000-22222-2-200020-20000000000000000000
χ322222-2-222-2-22222-2-20022-2-2-2-2-2200000000000-22-2-2222000-2020000000000000000000
χ332222-2-22-222-2222-2-222-2-22222000000-20022-2-2-2200-200220000000000000000-2000000
χ342222-2-22-222-2222-2-222-2-222-2-2000000-20022-2-22-200200-2-200000000000000002000000
χ352222-2-22-222-2222-2-2-2-2-2-22222000000200-2-222-2200-200-2-200000000000000002000000
χ362222-2-22-222-2222-2-2-2-2-2-222-2-2000000200-2-2222-200200220000000000000000-2000000
χ3722-2-22-22-22-222-2-22-2002-22-200002i−2i000000000002i−2i02i−2i0000002i−2i00000000000002-200
χ3822-2-22-22-22-222-2-22-2002-22-200002i−2i00000000000−2i2i0−2i2i0000002i−2i0000000000000-2200
χ3922-2-22-22-22-222-2-22-2002-22-20000−2i2i000000000002i−2i02i−2i000000−2i2i0000000000000-2200
χ4022-2-22-22-22-222-2-22-2002-22-20000−2i2i00000000000−2i2i0−2i2i000000−2i2i00000000000002-200
χ4122-2-2-222-2-2222-2-2-22002-2-220000002i−2i0000000002i−2i0−2i2i0000000000002i−2i002-20000000
χ4222-2-2-222-2-2222-2-2-22002-2-220000002i−2i000000000−2i2i02i−2i0000000000002i−2i00-220000000
χ4322-2-2-222-2-2222-2-2-22002-2-22000000−2i2i0000000002i−2i0−2i2i000000000000−2i2i00-220000000
χ4422-2-2-222-2-2222-2-2-22002-2-22000000−2i2i000000000−2i2i02i−2i000000000000−2i2i002-20000000
χ45444444-2-4-4-4-4-2-2-2-2-20022220000000004i−4i000000000000000000000−2i2i0000000000000
χ46444444-2-4-4-4-4-2-2-2-2-2002222000000000−4i4i0000000000000000000002i−2i0000000000000
χ474444-4-4-24-4-44-2-2-22200-2-222004-4000000000000000000000-2020000000000000000000
χ484444-4-4-24-4-44-2-2-22200-2-22200-4400000000000000000000020-20000000000000000000
χ494444-4-4-2-444-4-2-2-2224422-2-200000000-400-2-22200000000000000000000000000000000
χ504444-4-4-2-444-4-2-2-222-4-422-2-20000000040022-2-200000000000000000000000000000000
χ5144-4-44-444-44-44-4-44-400-44-4400000000000000000000000000000000000000000000000
χ5244-4-44-4-24-44-4-222-22002-22-200000000000000000000000000000000000023−23000000000
χ5344-4-44-4-24-44-4-222-22002-22-2000000000000000000000000000000000000−2323000000000
χ5444-4-44-4-2-44-44-222-2200-22-2200004i−4i0000000000000000000000−2i2i00000000000000000
χ5544-4-44-4-2-44-44-222-2200-22-220000−4i4i00000000000000000000002i−2i00000000000000000
χ5644-4-4-44444-4-44-4-4-4400-444-400000000000000000000000000000000000000000000000
χ5744-4-4-44-244-4-4-2222-2002-2-2200000000000000000000000000000023−23000000000000000
χ5844-4-4-44-244-4-4-2222-2002-2-22000000000000000000000000000000−2323000000000000000
χ5944-4-4-44-2-4-444-2222-200-222-20000004i−4i00000000000000000000000000−2i2i00000000000
χ6044-4-4-44-2-4-444-2222-200-222-2000000−4i4i000000000000000000000000002i−2i00000000000
χ614-4-440040000-44-400−2i22i200004-4000000000−2i22i2000000000−2i22i200000000000000000000000
χ624-4-440040000-44-400−2i22i20000-44000000000−2i22i20000000002i2−2i200000000000000000000000
χ634-4-440040000-44-4002i2−2i200004-40000000002i2−2i20000000002i2−2i200000000000000000000000
χ644-4-440040000-44-4002i2−2i20000-440000000002i2−2i2000000000−2i22i200000000000000000000000
χ658-88-80080000-8-880000000000000000000000000000000000000000000000000000000
χ668-88-800-4000044-400000000000000000000026−2600000000000000000000000000000000
χ678-88-800-4000044-4000000000000000000000−262600000000000000000000000000000000
χ688-8-8800-400004-4400−4i24i20000000000000002i2−2i20000000000000000000000000000000000
χ698-8-8800-400004-44004i2−4i2000000000000000−2i22i20000000000000000000000000000000000

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