Finite Group Databasebeta

← Group #10698760

Character table — Group #10698760

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order1222223444444666444661212121212121212224466661212121212128888242424242424242488888888888822
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1
χ92222222222-2-22222-2-2-22222-2-2-2-22222-2-22222-2-2-2-2-2-200000000000000000000000000
χ102222222222-2-22222-2-2-22222-2-2-2-222-2-222-2-2-2-2-2-2222200000000000000000000000000
χ112222222-2-2-222-2222-22-222-2-22222-2-200000000-2-200002i−2i002i2i−2i−2i000000000000000000
χ122222222-2-2-222-2222-22-222-2-22222-2-200000000-2-20000−2i2i00−2i−2i2i2i000000000000000000
χ132222222-2-2-2-2-2-22222-2222-2-2-2-2-2-2-2-200000000220000002i−2i00002i2i−2i−2i00000000000000
χ142222222-2-2-2-2-2-22222-2222-2-2-2-2-2-2-2-20000000022000000−2i2i0000−2i−2i2i2i00000000000000
χ15222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ16222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ17222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-1-1111122-2-2-1-1-1-1111100000000000000
χ18222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-1-11111-2-2221111-1-1-1-100000000000000
χ19222222-1222-2-22-1-1-1-2-2-2-1-1-1-11111-1-122-2-2-1-1-1-11111110000−i3i3−i3i3−i3i3−i3i300000000000000
χ20222222-1222-2-22-1-1-1-2-2-2-1-1-1-11111-1-122-2-2-1-1-1-11111110000i3−i3i3−i3i3−i3i3−i300000000000000
χ21222222-1222-2-22-1-1-1-2-2-2-1-1-1-11111-1-1-2-222111111-1-1-1-10000−i3i3−i3i3i3−i3i3−i300000000000000
χ22222222-1222-2-22-1-1-1-2-2-2-1-1-1-11111-1-1-2-222111111-1-1-1-10000i3−i3i3−i3−i3i3−i3i300000000000000
χ23222222-1-2-2-222-2-1-1-1-22-2-1-111-1-1-1-1110000−i3−i3i3i311−i3−i3i3i32i−2i00−i−iii3−3−3300000000000000
χ24222222-1-2-2-222-2-1-1-1-22-2-1-111-1-1-1-1110000−i3−i3i3i311−i3−i3i3i3−2i2i00ii−i−i−333−300000000000000
χ25222222-1-2-2-222-2-1-1-1-22-2-1-111-1-1-1-1110000i3i3−i3−i311i3i3−i3−i32i−2i00−i−iii−333−300000000000000
χ26222222-1-2-2-222-2-1-1-1-22-2-1-111-1-1-1-1110000i3i3−i3−i311i3i3−i3−i3−2i2i00ii−i−i3−3−3300000000000000
χ27222222-1-2-2-2-2-2-2-1-1-12-22-1-1111111110000−i3−i3i3i3-1-1i3i3−i3−i3002i−2i3−3−33−i−iii00000000000000
χ28222222-1-2-2-2-2-2-2-1-1-12-22-1-1111111110000−i3−i3i3i3-1-1i3i3−i3−i300−2i2i−333−3ii−i−i00000000000000
χ29222222-1-2-2-2-2-2-2-1-1-12-22-1-1111111110000i3i3−i3−i3-1-1−i3−i3i3i3002i−2i−333−3−i−iii00000000000000
χ30222222-1-2-2-2-2-2-2-1-1-12-22-1-1111111110000i3i3−i3−i3-1-1−i3−i3i3i300−2i2i3−3−33ii−i−i00000000000000
χ312222-2-2222-222-2222-2-22-2-22-222-2-22-2000000002-2000000000000000022-2-20000000000
χ322222-2-2222-222-2222-2-22-2-22-222-2-22-2000000002-20000000000000000-2-2220000000000
χ332222-2-2222-2-2-2-222222-2-2-22-2-2-2222-200000000-220000000000000000000000002i2i−2i−2i00
χ342222-2-2222-2-2-2-222222-2-2-22-2-2-2222-200000000-22000000000000000000000000−2i−2i2i2i00
χ352222-2-22-2-222222222-2-2-2-2-2222-2-2-2200000000-220000000000000000000022-2-2000000
χ362222-2-22-2-222222222-2-2-2-2-2222-2-2-2200000000-2200000000000000000000-2-222000000
χ372222-2-22-2-22-2-22222-222-2-2-22-2-222-22000000002-200000000000000000000000000002-2
χ382222-2-22-2-22-2-22222-222-2-2-22-2-222-22000000002-20000000000000000000000000000-22
χ3922-2-22-222-2200-22-2-20002-22-20000-22002i−2i0000002i−2i2i−2i000000000000−i2i2−i2i200002−22−200
χ4022-2-22-222-2200-22-2-20002-22-20000-22002i−2i0000002i−2i2i−2i000000000000i2−i2i2−i20000−22−2200
χ4122-2-22-222-2200-22-2-20002-22-20000-2200−2i2i000000−2i2i−2i2i000000000000−i2i2−i2i20000−22−2200
χ4222-2-22-222-2200-22-2-20002-22-20000-2200−2i2i000000−2i2i−2i2i000000000000i2−i2i2−i200002−22−200
χ4322-2-2-2222-2-20022-2-2000-22220000-2-22-2002-22-2000000000000000000−i2i2i2−i20000−i2i2i2−i200
χ4422-2-2-2222-2-20022-2-2000-22220000-2-22-2002-22-2000000000000000000i2−i2−i2i20000i2−i2−i2i200
χ4522-2-2-2222-2-20022-2-2000-22220000-2-2-2200-22-22000000000000000000−i2i2i2−i20000i2−i2−i2i200
χ4622-2-2-2222-2-20022-2-2000-22220000-2-2-2200-22-22000000000000000000i2−i2−i2i20000−i2i2i2−i200
χ474444-4-4-244-444-4-2-2-2-4-4422-22-2-222-2200000000-22000000000000000000000000000000
χ484444-4-4-244-4-4-4-4-2-2-244-422-2222-2-2-22000000002-2000000000000000000000000000000
χ494444-4-4-2-4-44444-2-2-24-4-4222-2-2-2222-2000000002-2000000000000000000000000000000
χ504444-4-4-2-4-44-4-44-2-2-2-444222-222-2-22-200000000-22000000000000000000000000000000
χ5144-4-44-44-44-40044-4-40004-4-4400004-40000000000000000000000000000000000000000
χ5244-4-44-4-24-4400-4-222000-22-2200002-2004i−4i000000−2i2i−2i2i00000000000000000000000000
χ5344-4-44-4-24-4400-4-222000-22-2200002-200−4i4i0000002i−2i2i−2i00000000000000000000000000
χ5444-4-44-4-2-44-4004-222000-222-20000-22000000000023−23−232300000000000000000000000000
χ5544-4-44-4-2-44-4004-222000-222-20000-220000000000−232323−2300000000000000000000000000
χ5644-4-4-444-44400-44-4-4000-44-4-40000440000000000000000000000000000000000000000
χ5744-4-4-44-24-4-4004-2220002-2-2-20000224-400-22-2200000000000000000000000000000000
χ5844-4-4-44-24-4-4004-2220002-2-2-2000022-44002-22-200000000000000000000000000000000
χ5944-4-4-44-2-44400-4-2220002-2220000-2-20000−2i32i32i3−2i300000000000000000000000000000000
χ6044-4-4-44-2-44400-4-2220002-2220000-2-200002i3−2i3−2i32i300000000000000000000000000000000
χ614-4-440040004-40-4-4400000004-400000000000000000000000000000000000022−22000000
χ624-4-440040004-40-4-4400000004-4000000000000000000000000000000000000−2222000000
χ634-4-44004000-440-4-440000000-44000000000000000000000000000000000022−2200000000
χ644-4-44004000-440-4-440000000-440000000000000000000000000000000000−222200000000
χ658-88-8008000000-88-800000000000000000000000000000000000000000000000000000
χ668-88-800-40000004-4400000000043−43000000000000000000000000000000000000000000
χ678-88-800-40000004-44000000000−4343000000000000000000000000000000000000000000
χ688-8-8800-40008-8044-40000000-4400000000000000000000000000000000000000000000
χ698-8-8800-4000-88044-400000004-400000000000000000000000000000000000000000000

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