Finite Group Databasebeta

← Group #10697233

Character table — Group #10697233

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order122222344444466644466121212121212121288881212242424242424242424446612121212121244448888888888
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
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-111111-1-1-1-11111-1-1-1-1-1-1-1-111
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-111111111-1-1
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
χ9222222222-2-2-2-22222-2-222-2-2-2-222-2-20000-2200000000000000000000000000002i2i−2i−2i00
χ10222222222-2-2-2-22222-2-222-2-2-2-222-2-20000-220000000000000000000000000000−2i−2i2i2i00
χ112222222-2-22222222-2-2-2222222-2-2-2-20000-2-20000000000000000000022-2-20000000000
χ122222222-2-22222222-2-2-2222222-2-2-2-20000-2-200000000000000000000-2-2220000000000
χ132222222-2-2-2-2-2-2222-22222-2-2-2-2-2-22222-2-22-22222-2-2-2-200000000000000000000000000
χ142222222-2-2-2-2-2-2222-22222-2-2-2-2-2-222-2-2222-2-2-2-2-2222200000000000000000000000000
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
χ19222222-1-2-2-2-2-2-2-1-1-1-222-1-1111111-1-122-2-2-11-1-1-1-111110000−i3i3−i3i3−i3−i3i3i300000000000000
χ20222222-1-2-2-2-2-2-2-1-1-1-222-1-1111111-1-122-2-2-11-1-1-1-111110000i3−i3i3−i3i3i3−i3−i300000000000000
χ21222222-1-2-2-2-2-2-2-1-1-1-222-1-1111111-1-1-2-222-111111-1-1-1-10000−i3i3−i3i3i3i3−i3−i300000000000000
χ22222222-1-2-2-2-2-2-2-1-1-1-222-1-1111111-1-1-2-222-111111-1-1-1-10000i3−i3i3−i3−i3−i3i3i300000000000000
χ232222-2-22222-22-2222-22-2-2-222-2-222220000-2-200000000200-222-2-2000000000000000000
χ242222-2-22222-22-2222-22-2-2-222-2-222220000-2-200000000-2002-2-222000000000000000000
χ252222-2-2222-22-22222-2-22-2-2-2-22222-2-200002-200000000000000000000000022-2-2000000
χ262222-2-2222-22-22222-2-22-2-2-2-22222-2-200002-2000000000000000000000000-2-222000000
χ272222-2-22-2-22-22-22222-22-2-222-2-2-2-2-2-2000022000000000000000000000000000000002-2
χ282222-2-22-2-22-22-22222-22-2-222-2-2-2-2-2-200002200000000000000000000000000000000-22
χ292222-2-22-2-2-22-2222222-2-2-2-2-222-2-2220000-220000000002-2000002-22-200000000000000
χ302222-2-22-2-2-22-2222222-2-2-2-2-222-2-2220000-22000000000-2200000-22-2200000000000000
χ312222-2-2-1222-22-2-1-1-1-22-211-1-111-1-1-1-1000011−i3−i3i3i3−i3−i3i3i3200-2-1-111−i3i3i3−i300000000000000
χ322222-2-2-1222-22-2-1-1-1-22-211-1-111-1-1-1-1000011−i3−i3i3i3−i3−i3i3i3-200211-1-1i3−i3−i3i300000000000000
χ332222-2-2-1222-22-2-1-1-1-22-211-1-111-1-1-1-1000011i3i3−i3−i3i3i3−i3−i3200-2-1-111i3−i3−i3i300000000000000
χ342222-2-2-1222-22-2-1-1-1-22-211-1-111-1-1-1-1000011i3i3−i3−i3i3i3−i3−i3-200211-1-1−i3i3i3−i300000000000000
χ352222-2-2-1-2-2-22-22-1-1-122-21111-1-111-1-100001-1−i3−i3i3i3i3i3−i3−i302-20−i3i3i3−i3-11-1100000000000000
χ362222-2-2-1-2-2-22-22-1-1-122-21111-1-111-1-100001-1−i3−i3i3i3i3i3−i3−i30-220i3−i3−i3i31-11-100000000000000
χ372222-2-2-1-2-2-22-22-1-1-122-21111-1-111-1-100001-1i3i3−i3−i3−i3−i3i3i302-20i3−i3−i3i3-11-1100000000000000
χ382222-2-2-1-2-2-22-22-1-1-122-21111-1-111-1-100001-1i3i3−i3−i3−i3−i3i3i30-220−i3i3i3−i31-11-100000000000000
χ392-2-222-22002-2-22-22-20002-22-22-20000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i20000000000002i−2i0000002−22−200
χ402-2-222-22002-2-22-22-20002-22-22-20000−i2i2−i2i200−i2i2−i2i2−i2i2−i2i2000000000000−2i2i000000−22−2200
χ412-2-222-22002-2-22-22-20002-22-22-20000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i20000000000002i−2i000000−22−2200
χ422-2-222-22002-2-22-22-20002-22-22-20000i2−i2i2−i200i2−i2i2−i2i2−i2i2−i2000000000000−2i2i0000002−22−200
χ432-2-222-2200-222-2-22-20002-2-22-220000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i2000000000000002-20000−i2i2i2−i200
χ442-2-222-2200-222-2-22-20002-2-22-220000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i200000000000000-220000i2−i2−i2i200
χ452-2-222-2200-222-2-22-20002-2-22-220000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i2000000000000002-20000i2−i2−i2i200
χ462-2-222-2200-222-2-22-20002-2-22-220000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i200000000000000-220000−i2i2i2−i200
χ47444444-244-4-4-4-4-2-2-24-4-4-2-22222-2-22200002-20000000000000000000000000000000000
χ48444444-2-4-44444-2-2-2-4-4-4-2-2-2-2-2-222220000220000000000000000000000000000000000
χ494444-4-4-244-44-44-2-2-2-4-442222-2-2-2-2220000-220000000000000000000000000000000000
χ504444-4-4-2-4-44-44-4-2-2-24-4422-2-22222220000-2-20000000000000000000000000000000000
χ5144-4-40044-40000-4-440000000004-40000000000000000000000000000000000−2i22i2000000
χ5244-4-40044-40000-4-440000000004-400000000000000000000000000000000002i2−2i2000000
χ5344-4-4004-440000-4-44000000000-4400000000000000000000000000000000−2i22i200000000
χ5444-4-4004-440000-4-44000000000-44000000000000000000000000000000002i2−2i200000000
χ554-4-444-4-2004-4-442-22000-22-22-220000−2i22i2−2i22i200i2−i2i2−i2i2−i2i2−i200000000000000000000000000
χ564-4-444-4-2004-4-442-22000-22-22-2200002i2−2i22i2−2i200−i2i2−i2i2−i2i2−i2i200000000000000000000000000
χ574-4-444-4-200-444-42-22000-222-22-20000−2i22i22i2−2i200i2−i2i2−i2−i2i2−i2i200000000000000000000000000
χ584-4-444-4-200-444-42-22000-222-22-200002i2−2i2−2i22i200−i2i2−i2i2i2−i2i2−i200000000000000000000000000
χ594-4-44-4440044-4-4-44-4000-444-4-4400000000000000000000000000000000000000000000
χ604-4-44-44400-4-444-44-4000-44-444-400000000000000000000000000000000000000000000
χ614-4-44-44-20044-4-42-220002-2-222-200000000006−6−666−6−6600000000000000000000000000
χ624-4-44-44-20044-4-42-220002-2-222-20000000000−666−6−666−600000000000000000000000000
χ634-4-44-44-200-4-4442-220002-22-2-2200000000006−6−66−666−600000000000000000000000000
χ644-4-44-44-200-4-4442-220002-22-2-220000000000−666−66−6−6600000000000000000000000000
χ6588-8-800-48-8000044-4000000000-44000000000000000000000000000000000000000000
χ6688-8-800-4-88000044-40000000004-4000000000000000000000000000000000000000000
χ678-88-80080000008-8-800000000000000000000000000000000000000000000000000000
χ688-88-800-4000000-44400000000000−4i34i30000000000000000000000000000000000000000
χ698-88-800-4000000-444000000000004i3−4i30000000000000000000000000000000000000000

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