Finite Group Databasebeta

← Group #10691713

Character table — Group #10691713

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222222444444444444488888888888888888812121212121212121616161616161616161624242424242424244848
order12222234444446664446612121212121212124444888812122424242424242424888888884412121212121212128888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111
χ511111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ611111111111111111111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-111-1-111
χ811111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-111-1-1
χ91111111-1-1-1-1-1-11111-1111-1-1-1-1-1-1111-11-111-1-11-11111-1-1-1-1ii−i−iii−i−i1-11-11-111-1-1ii−i−ii−ii−ii−i
χ101111111-1-1-1-1-1-11111-1111-1-1-1-1-1-1111-11-111-1-11-11111-1-1-1-1−i−iii−i−iii1-11-11-111-1-1−i−iii−ii−ii−ii
χ111111111-1-1-1-1-1-11111-1111-1-1-1-1-1-1111-11-1-1-1111-1-1-1-1-11111ii−i−iii−i−i-111-11-1-1-111−i−iiii−ii−i−ii
χ121111111-1-1-1-1-1-11111-1111-1-1-1-1-1-1111-11-1-1-1111-1-1-1-1-11111−i−iii−i−iii-111-11-1-1-111ii−i−i−ii−iii−i
χ131111111-1-1-1-1-1-11111-1111-1-1-1-1-1-111-11-1111-1-11-11111-1-1-1-1ii−i−i−i−iii-11-11-11-1-111ii−i−ii−i−ii−ii
χ141111111-1-1-1-1-1-11111-1111-1-1-1-1-1-111-11-1111-1-11-11111-1-1-1-1−i−iiiii−i−i-11-11-11-1-111−i−iii−iii−ii−i
χ151111111-1-1-1-1-1-11111-1111-1-1-1-1-1-111-11-11-1-1111-1-1-1-1-11111ii−i−i−i−iii1-1-11-1111-1-1−i−iiii−i−iii−i
χ161111111-1-1-1-1-1-11111-1111-1-1-1-1-1-111-11-11-1-1111-1-1-1-1-11111−i−iiiii−i−i1-1-11-1111-1-1ii−i−i−iii−i−ii
χ1722222222-222-22222-2-2-2222222-2-2-2-200000000-2-2000000002222000000000000000000-2-20000
χ1822222222-222-22222-2-2-2222222-2-2-2-200000000-2-200000000-2-2-2-2000000000000000000220000
χ192222222-22-2-22-2222-22-222-2-2-2-222-2-200000000-22000000002i2i−2i−2i000000000000000000−2i2i0000
χ202222222-22-2-22-2222-22-222-2-2-2-222-2-200000000-2200000000−2i−2i2i2i0000000000000000002i−2i0000
χ21222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-1-1-10000000000
χ22222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-11111111100000000-2-2-1-1-1-111110000000000
χ23222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-100000000-2-2111111110000000000
χ24222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-11111111100000000221111-1-1-1-10000000000
χ25222222-1-2-2-2-2-2-2-1-1-12-22-1-1111111-1-12-22-222-2-2-11-1-1-1-11111000000002-2-11-11-1-1110000000000
χ26222222-1-2-2-2-2-2-2-1-1-12-22-1-1111111-1-12-22-2-2-222-111111-1-1-1-100000000-22-11-1111-1-10000000000
χ27222222-1-2-2-2-2-2-2-1-1-12-22-1-1111111-1-1-22-2222-2-2-11-1-1-1-1111100000000-221-11-111-1-10000000000
χ28222222-1-2-2-2-2-2-2-1-1-12-22-1-1111111-1-1-22-22-2-222-111111-1-1-1-1000000002-21-11-1-1-1110000000000
χ292222-2-2222-222-2222-2-22-2-222-2-2222222-2-20000-2-200000000000000000022-2-200000000000000
χ302222-2-2222-222-2222-2-22-2-222-2-22222-2-2220000-2-2000000000000000000-2-22200000000000000
χ312222-2-222-2-22-2-222222-2-2-222-2-2-2-2-2-200000000220000000000002i2i−2i−2i0000000000000000−2i2i00
χ322222-2-222-2-22-2-222222-2-2-222-2-2-2-2-2-20000000022000000000000−2i−2i2i2i00000000000000002i−2i00
χ332222-2-22-222-2222222-2-2-2-2-2-22222-2-2000000002-200000000000022220000000000000000-2-200
χ342222-2-22-222-2222222-2-2-2-2-2-22222-2-2000000002-2000000000000-2-2-2-200000000000000002200
χ352222-2-22-2-22-2-22222-222-2-2-2-222-2-2222-2-220000-220000000000000000002-2-2200000000000000
χ362222-2-22-2-22-2-22222-222-2-2-2-222-2-222-222-20000-22000000000000000000-222-200000000000000
χ372222-2-2-122-222-2-1-1-1-2-2211-1-111-1-1-1-122-2-2000011−i3−i3i3i3−i3−i3i3i30000000000-1-111−i3i3−i3i30000000000
χ382222-2-2-122-222-2-1-1-1-2-2211-1-111-1-1-1-122-2-2000011i3i3−i3−i3i3i3−i3−i30000000000-1-111i3−i3i3−i30000000000
χ392222-2-2-122-222-2-1-1-1-2-2211-1-111-1-1-1-1-2-222000011−i3−i3i3i3−i3−i3i3i3000000000011-1-1i3−i3i3−i30000000000
χ402222-2-2-122-222-2-1-1-1-2-2211-1-111-1-1-1-1-2-222000011i3i3−i3−i3i3i3−i3−i3000000000011-1-1−i3i3−i3i30000000000
χ412222-2-2-1-2-22-2-22-1-1-1-2221111-1-111-1-12-2-2200001-1−i3−i3i3i3i3i3−i3−i30000000000-111-1−i3i3i3−i30000000000
χ422222-2-2-1-2-22-2-22-1-1-1-2221111-1-111-1-12-2-2200001-1i3i3−i3−i3−i3−i3i3i30000000000-111-1i3−i3−i3i30000000000
χ432222-2-2-1-2-22-2-22-1-1-1-2221111-1-111-1-1-222-200001-1−i3−i3i3i3i3i3−i3−i300000000001-1-11i3−i3−i3i30000000000
χ442222-2-2-1-2-22-2-22-1-1-1-2221111-1-111-1-1-222-200001-1i3i3−i3−i3−i3−i3i3i300000000001-1-11−i3i3i3−i30000000000
χ4522-2-22-22202-20-22-2-20002-22-22-2000000002−22−2002−22−22−22−22-22-2000000000000002−22−2000000
χ4622-2-22-22202-20-22-2-20002-22-22-2000000002−22−2002−22−22−22−2-22-2200000000000000−22−22000000
χ4722-2-22-22202-20-22-2-20002-22-22-200000000−22−2200−22−22−22−222-22-200000000000000−22−22000000
χ4822-2-22-22202-20-22-2-20002-22-22-200000000−22−2200−22−22−22−22-22-22000000000000002−22−2000000
χ4922-2-22-22-20-22022-2-20002-2-22-22000000002−2−22002−22−2−22−222i−2i−2i2i00000000000000i2−i2−i2i2000000
χ5022-2-22-22-20-22022-2-20002-2-22-22000000002−2−22002−22−2−22−22−2i2i2i−2i00000000000000−i2i2i2−i2000000
χ5122-2-22-22-20-22022-2-20002-2-22-2200000000−222−200−22−222−22−22i−2i−2i2i00000000000000−i2i2i2−i2000000
χ5222-2-22-22-20-22022-2-20002-2-22-2200000000−222−200−22−222−22−2−2i2i2i−2i00000000000000i2−i2−i2i2000000
χ53444444-24-444-44-2-2-2-4-4-4-2-2-2-2-2-222220000000022000000000000000000000000000000000000
χ54444444-2-44-4-44-4-2-2-2-44-4-2-22222-2-222000000002-2000000000000000000000000000000000000
χ554444-4-4-24-4-44-4-4-2-2-244-422-2-222222200000000-2-2000000000000000000000000000000000000
χ564444-4-4-2-444-444-2-2-24-4-42222-2-2-2-22200000000-22000000000000000000000000000000000000
χ5744-4-44-4-2404-40-4-222000-22-22-220000000022−2222−2200−22−22−22−220000000000000000000000000000
χ5844-4-44-4-2404-40-4-222000-22-22-2200000000−2222−2222002−22−22−22−20000000000000000000000000000
χ5944-4-44-4-2-40-4404-222000-222-22-20000000022−22−222200−22−222−22−20000000000000000000000000000
χ6044-4-44-4-2-40-4404-222000-222-22-200000000−222222−22002−22−2−22−220000000000000000000000000000
χ6144-4-4-44440-4-4044-4-4000-444-4-4400000000000000000000000000000000000000000000000000
χ6244-4-4-444-40440-44-4-4000-44-444-400000000000000000000000000000000000000000000000000
χ6344-4-4-44-240-4-404-2220002-2-222-200000000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000000000
χ6444-4-4-44-240-4-404-2220002-2-222-200000000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000000000
χ6544-4-4-44-2-40440-4-2220002-22-2-2200000000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ6644-4-4-44-2-40440-4-2220002-22-2-2200000000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ674-4-440040400-40-4-440000000004-4000000000000000000000000−2i22i2−2i22i200000000000000000000
χ684-4-440040400-40-4-440000000004-40000000000000000000000002i2−2i22i2−2i200000000000000000000
χ694-4-440040-40040-4-44000000000-4400000000000000000000000022−22−222200000000000000000000
χ704-4-440040-40040-4-44000000000-44000000000000000000000000−222222−2200000000000000000000
χ718-88-8008000000-88-800000000000000000000000000000000000000000000000000000000000
χ728-88-800-40000004-4400000000000−4i34i30000000000000000000000000000000000000000000000
χ738-88-800-40000004-44000000000004i3−4i30000000000000000000000000000000000000000000000
χ748-8-8800-40800-8044-4000000000-44000000000000000000000000000000000000000000000000
χ758-8-8800-40-8008044-40000000004-4000000000000000000000000000000000000000000000000

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