Finite Group Databasebeta

← Group #10697311

Character table — Group #10697311

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order122222344444466644466121212121212121288881212242424242424242424446612121212121244448888888824
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-111111-1-1-1-11111-1-1-1-11111-1-1
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111111111-1-1-1-1-1-1
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ922222222-2-2-2-22222-22-222-2-2-2-222-2-20000-2200000000000000000000000022-2-2000000
χ1022222222-2-2-2-22222-22-222-2-2-2-222-2-20000-22000000000000000000000000-2-222000000
χ112222222-22222-2222-2-2-222-2-222-2-22222-2-2-2-22222-2-2-2-200000000000000000000000000
χ122222222-22222-2222-2-2-222-2-222-2-222-2-222-2-2-2-2-2-2222200000000000000000000000000
χ132222222-2-2-2-2-2-22222-222222-2-2-2-2-2-200002-2000000000000000000000000000022-2-200
χ142222222-2-2-2-2-2-22222-222222-2-2-2-2-2-200002-20000000000000000000000000000-2-22200
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
χ17222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111112-2-22-1-1-1-1111100000000000000
χ18222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-222-21111-1-1-1-100000000000000
χ19222222-1-22222-2-1-1-1-2-2-2-1-111-1-111-1-122-2-211-1-1-1-111110000−i3i3−i3i3−i3−i3i3i300000000000000
χ20222222-1-22222-2-1-1-1-2-2-2-1-111-1-111-1-122-2-211-1-1-1-111110000i3−i3i3−i3i3i3−i3−i300000000000000
χ21222222-1-22222-2-1-1-1-2-2-2-1-111-1-111-1-1-2-222111111-1-1-1-10000−i3i3−i3i3i3i3−i3−i300000000000000
χ22222222-1-22222-2-1-1-1-2-2-2-1-111-1-111-1-1-2-222111111-1-1-1-10000i3−i3i3−i3−i3−i3i3i300000000000000
χ232222-2-22222-2-22222-2-22-2-2-2-22222-2-200002-2000000000000000000000000000000002-2
χ242222-2-22222-2-22222-2-22-2-2-2-22222-2-200002-200000000000000000000000000000000-22
χ252222-2-222-2-22222222-2-2-2-222-2-222220000-2-200000000200-222-2-2000000000000000000
χ262222-2-222-2-22222222-2-2-2-222-2-222220000-2-200000000-2002-2-222000000000000000000
χ272222-2-22-222-2-2-222222-2-2-22222-2-2-2-20000-22000000000000000000002i2i−2i−2i0000000000
χ282222-2-22-222-2-2-222222-2-2-22222-2-2-2-20000-2200000000000000000000−2i−2i2i2i0000000000
χ292222-2-22-2-2-222-2222-222-2-2-2-2-2-2-2-2220000220000000002-2000002-22-200000000000000
χ302222-2-22-2-2-222-2222-222-2-2-2-2-2-2-2-222000022000000000-2200000-22-2200000000000000
χ312222-2-2-12-2-2222-1-1-12-2-211-1-111-1-1-1-1000011−i3−i3i3i3−i3−i3i3i3200-2-1-111−i3i3i3−i300000000000000
χ322222-2-2-12-2-2222-1-1-12-2-211-1-111-1-1-1-1000011−i3−i3i3i3−i3−i3i3i3-200211-1-1i3−i3−i3i300000000000000
χ332222-2-2-12-2-2222-1-1-12-2-211-1-111-1-1-1-1000011i3i3−i3−i3i3i3−i3−i3200-2-1-111i3−i3−i3i300000000000000
χ342222-2-2-12-2-2222-1-1-12-2-211-1-111-1-1-1-1000011i3i3−i3−i3i3i3−i3−i3-200211-1-1−i3i3i3−i300000000000000
χ352222-2-2-1-2-2-222-2-1-1-1-22211111111-1-10000-1-1−i3−i3i3i3i3i3−i3−i302-20−i3i3i3−i3-11-1100000000000000
χ362222-2-2-1-2-2-222-2-1-1-1-22211111111-1-10000-1-1−i3−i3i3i3i3i3−i3−i30-220i3−i3−i3i31-11-100000000000000
χ372222-2-2-1-2-2-222-2-1-1-1-22211111111-1-10000-1-1i3i3−i3−i3−i3−i3i3i302-20i3−i3−i3i3-11-1100000000000000
χ382222-2-2-1-2-2-222-2-1-1-1-22211111111-1-10000-1-1i3i3−i3−i3−i3−i3i3i30-220−i3i3i3−i31-11-100000000000000
χ392-2-222-2202-22-20-22-20002-2002-2002-2002i−2i0000002i−2i2i−2i00000000000000002−22−2−i2i2−i2i200
χ402-2-222-2202-22-20-22-20002-2002-2002-2002i−2i0000002i−2i2i−2i0000000000000000−22−22i2−i2i2−i200
χ412-2-222-2202-22-20-22-20002-2002-2002-200−2i2i000000−2i2i−2i2i00000000000000002−22−2i2−i2i2−i200
χ422-2-222-2202-22-20-22-20002-2002-2002-200−2i2i000000−2i2i−2i2i0000000000000000−22−22−i2i2−i2i200
χ432-2-222-220-22-220-22-20002-200-2200-222i−2i00002i−2i2i−2i000000000000000000002−2−22−i2i2i2−i200
χ442-2-222-220-22-220-22-20002-200-2200-222i−2i00002i−2i2i−2i00000000000000000000−222−2i2−i2−i2i200
χ452-2-222-220-22-220-22-20002-200-2200-22−2i2i0000−2i2i−2i2i000000000000000000002−2−22i2−i2−i2i200
χ462-2-222-220-22-220-22-20002-200-2200-22−2i2i0000−2i2i−2i2i00000000000000000000−222−2−i2i2i2−i200
χ47444444-24-4-4-4-44-2-2-2-44-4-2-22222-2-22200002-20000000000000000000000000000000000
χ48444444-2-4-4-4-4-4-4-2-2-24-44-2-2-2-22222220000-220000000000000000000000000000000000
χ494444-4-4-2444-4-44-2-2-2-4-442222-2-2-2-2220000-220000000000000000000000000000000000
χ504444-4-4-2-444-4-4-4-2-2-244-422-2-2-2-2222200002-20000000000000000000000000000000000
χ514-44-400440000-4-4-440000000004-400000000000000000000000000002i−2i2i−2i0000000000
χ524-44-400440000-4-4-440000000004-40000000000000000000000000000−2i2i−2i2i0000000000
χ534-44-4004-400004-4-44000000000-4400000000000000000000000000002-2-220000000000
χ544-44-4004-400004-4-44000000000-440000000000000000000000000000-222-20000000000
χ554-4-444-4-204-44-402-22000-2200-2200-22004i−4i000000−2i2i−2i2i00000000000000000000000000
χ564-4-444-4-204-44-402-22000-2200-2200-2200−4i4i0000002i−2i2i−2i00000000000000000000000000
χ574-4-444-4-20-44-4402-22000-22002-2002-24i−4i0000−2i2i−2i2i000000000000000000000000000000
χ584-4-444-4-20-44-4402-22000-22002-2002-2−4i4i00002i−2i2i−2i000000000000000000000000000000
χ594-4-44-44404-4-440-44-4000-44004-400-440000000000000000000000000000000000000000
χ604-4-44-4440-444-40-44-4000-4400-44004-40000000000000000000000000000000000000000
χ614-4-44-44-204-4-4402-220002-200-22002-200000023−23−2323000000000000000000000000000000
χ624-4-44-44-204-4-4402-220002-200-22002-2000000−232323−23000000000000000000000000000000
χ634-4-44-44-20-444-402-220002-2002-200-22000000000023−23−232300000000000000000000000000
χ644-4-44-44-20-444-402-220002-2002-200-220000000000−232323−2300000000000000000000000000
χ6588-8-80080000008-8-800000000000000000000000000000000000000000000000000000
χ6688-8-800-4000000-44400000−4i34i30000000000000000000000000000000000000000000000
χ6788-8-800-4000000-444000004i3−4i30000000000000000000000000000000000000000000000
χ688-88-800-480000-844-4000000000-44000000000000000000000000000000000000000000
χ698-88-800-4-80000844-40000000004-4000000000000000000000000000000000000000000

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