Finite Group Databasebeta

← Group #10697348

Character table — Group #10697348

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order122222344444466644466121212121212121288881212242424242424242424446612121212121244448888888844
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
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-111111-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1-111111111-1-1-1-11111-1-1
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ922222222-2-22-2-22222-2-222222-2-2-2-2222-2-2-2-22222-2-2-2-200000000000000000000000000
χ1022222222-2-22-2-22222-2-222222-2-2-2-22-2-222-2-2-2-2-2-2222200000000000000000000000000
χ112222222-222-222222-2-2-222-2-2-22222-20000-2-200000000000000000000000022-2-2000000
χ122222222-222-222222-2-2-222-2-2-22222-20000-2-2000000000000000000000000-2-222000000
χ132222222-2-2-2-2-2-2222-22222-2-2-2-2-2-2-2-2000022000000000000000000000000000022-2-200
χ142222222-2-2-2-2-2-2222-22222-2-2-2-2-2-2-2-20000220000000000000000000000000000-2-22200
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
χ19222222-12-2-22-2-2-1-1-12-2-2-1-1-1-1-11111-122-2-211-1-1-1-111110000−i3i3−i3i3−i3−i3i3i300000000000000
χ20222222-12-2-22-2-2-1-1-12-2-2-1-1-1-1-11111-122-2-211-1-1-1-111110000i3−i3i3−i3i3i3−i3−i300000000000000
χ21222222-12-2-22-2-2-1-1-12-2-2-1-1-1-1-11111-1-2-222111111-1-1-1-10000−i3i3−i3i3i3i3−i3−i300000000000000
χ22222222-12-2-22-2-2-1-1-12-2-2-1-1-1-1-11111-1-2-222111111-1-1-1-10000i3−i3i3−i3−i3−i3i3i300000000000000
χ232222-2-222222-2-2222-2-22-2-22-2-222-2-2200002-200000000200-222-2-2000000000000000000
χ242222-2-222222-2-2222-2-22-2-22-2-222-2-2200002-200000000-2002-2-222000000000000000000
χ252222-2-222-2-2222222-22-2-2-22-2-2-2-22220000-220000000002-2000002-22-200000000000000
χ262222-2-222-2-2222222-22-2-2-22-2-2-2-22220000-22000000000-2200000-22-2200000000000000
χ272222-2-22-222-2-2-222222-2-2-2-22222-2-2-20000-22000000000000000000002i2i−2i−2i0000000000
χ282222-2-22-222-2-2-222222-2-2-2-22222-2-2-20000-2200000000000000000000−2i−2i2i2i0000000000
χ292222-2-22-2-2-2-2222222-22-2-2-222-2-222-200002-2000000000000000000000000000000002-2
χ302222-2-22-2-2-2-2222222-22-2-2-222-2-222-200002-200000000000000000000000000000000-22
χ312222-2-2-12222-2-2-1-1-1-2-2211-111-1-111-10000-11−i3−i3i3i3−i3−i3i3i3200-2-1-111−i3i3i3−i300000000000000
χ322222-2-2-12222-2-2-1-1-1-2-2211-111-1-111-10000-11−i3−i3i3i3−i3−i3i3i3-200211-1-1i3−i3−i3i300000000000000
χ332222-2-2-12222-2-2-1-1-1-2-2211-111-1-111-10000-11i3i3−i3−i3i3i3−i3−i3200-2-1-111i3−i3−i3i300000000000000
χ342222-2-2-12222-2-2-1-1-1-2-2211-111-1-111-10000-11i3i3−i3−i3i3i3−i3−i3-200211-1-1−i3i3i3−i300000000000000
χ352222-2-2-12-2-2222-1-1-1-22-211-11111-1-1-100001-1−i3−i3i3i3i3i3−i3−i302-20−i3i3i3−i3-11-1100000000000000
χ362222-2-2-12-2-2222-1-1-1-22-211-11111-1-1-100001-1−i3−i3i3i3i3i3−i3−i30-220i3−i3−i3i31-11-100000000000000
χ372222-2-2-12-2-2222-1-1-1-22-211-11111-1-1-100001-1i3i3−i3−i3−i3−i3i3i302-20i3−i3−i3i3-11-1100000000000000
χ382222-2-2-12-2-2222-1-1-1-22-211-11111-1-1-100001-1i3i3−i3−i3−i3−i3i3i30-220−i3i3i3−i31-11-100000000000000
χ392-2-222-2202-202-22-2-20002-20002-22-20−i2i2−i2i200−i2i2−i2i2−i2i2−i2i20000000000000000002i−2i2−22−200
χ402-2-222-2202-202-22-2-20002-20002-22-20−i2i2−i2i200−i2i2−i2i2−i2i2−i2i2000000000000000000−2i2i−22−2200
χ412-2-222-2202-202-22-2-20002-20002-22-20i2−i2i2−i200i2−i2i2−i2i2−i2i2−i20000000000000000002i−2i−22−2200
χ422-2-222-2202-202-22-2-20002-20002-22-20i2−i2i2−i200i2−i2i2−i2i2−i2i2−i2000000000000000000−2i2i2−22−200
χ432-2-222-220-220-222-2-20002-2000-22-220−i2i2i2−i200−i2i2−i2i2i2−i2i2−i200000000000000002i−2i002−2−2200
χ442-2-222-220-220-222-2-20002-2000-22-220−i2i2i2−i200−i2i2−i2i2i2−i2i2−i20000000000000000−2i2i00−222−200
χ452-2-222-220-220-222-2-20002-2000-22-220i2−i2−i2i200i2−i2i2−i2−i2i2−i2i200000000000000002i−2i00−222−200
χ462-2-222-220-220-222-2-20002-2000-22-220i2−i2−i2i200i2−i2i2−i2−i2i2−i2i20000000000000000−2i2i002−2−2200
χ47444444-2-444-444-2-2-2-4-4-4-2-2222-2-2-2-220000220000000000000000000000000000000000
χ48444444-2-4-4-4-4-4-4-2-2-2-444-2-2222222220000-2-20000000000000000000000000000000000
χ494444-4-4-2-444-4-4-4-2-2-244-4222-2-2-2-222200002-20000000000000000000000000000000000
χ504444-4-4-2-4-4-4-444-2-2-24-44222-2-222-2-220000-220000000000000000000000000000000000
χ5144-4-4004400-400-44-4000004000000-4000000000000000000000000002-22-20000000000
χ5244-4-4004400-400-44-4000004000000-400000000000000000000000000-22-220000000000
χ5344-4-4004-400400-44-400000-40000004000000000000000000000000002i−2i−2i2i0000000000
χ5444-4-4004-400400-44-400000-4000000400000000000000000000000000−2i2i2i−2i0000000000
χ554-4-444-4-204-404-4-222000-22000-22-220−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ564-4-444-4-204-404-4-222000-22000-22-2202i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ574-4-444-4-20-440-44-222000-220002-22-20−2i22i22i2−2i200i2−i2i2−i2−i2i2−i2i200000000000000000000000000
χ584-4-444-4-20-440-44-222000-220002-22-202i2−2i2−2i22i200−i2i2−i2i2i2−i2i2−i200000000000000000000000000
χ594-4-44-44404-40-444-4-4000-440004-4-4400000000000000000000000000000000000000000
χ604-4-44-4440-4404-44-4-4000-44000-444-400000000000000000000000000000000000000000
χ614-4-44-44-204-40-44-2220002-2000-222-200000006−6−666−6−6600000000000000000000000000
χ624-4-44-44-204-40-44-2220002-2000-222-20000000−666−6−666−600000000000000000000000000
χ634-4-44-44-20-4404-4-2220002-20002-2-2200000006−6−66−666−600000000000000000000000000
χ644-4-44-44-20-4404-4-2220002-20002-2-220000000−666−66−6−6600000000000000000000000000
χ6588-8-800-4800-8004-4400000-400000040000000000000000000000000000000000000000
χ6688-8-800-4-8008004-44000004000000-40000000000000000000000000000000000000000
χ678-88-8008000000-8-8800000000000000000000000000000000000000000000000000000
χ688-88-800-400000044-400000043−43000000000000000000000000000000000000000000000
χ698-88-800-400000044-4000000−4343000000000000000000000000000000000000000000000

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