Finite Group Databasebeta

← Group #10691579

Character table — Group #10691579

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222222444444444444488888888888888888812121212121212121616161616161616161624242424242424244848
order12222234444446664446612121212121212128888888812122424242424242424224488888824242424242424242488888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ4111111111111111111111111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ511111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-11111-1-1
χ811111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-111
χ911111111-11-1-1-11111-1-111111-1-11-1-111-1-1ii−i−i-1-11111-1-1-1-111-1-1ii−i−ii−iii−i−iii−i−i1-1i−iii−i−i1-1
χ1011111111-11-1-1-11111-1-111111-1-11-1-111-1-1ii−i−i-1-11111-1-1-1-1-1-111−i−iiii−iii−i−iii−i−i-11−ii−i−iii-11
χ1111111111-11-1-1-11111-1-111111-1-11-1-111-1-1−i−iii-1-11111-1-1-1-111-1-1−i−iii−ii−i−iii−i−iii1-1−ii−i−iii1-1
χ1211111111-11-1-1-11111-1-111111-1-11-1-111-1-1−i−iii-1-11111-1-1-1-1-1-111ii−i−i−ii−i−iii−i−iii-11i−iii−i−i-11
χ1311111111-11-1-1-11111-1-111111-1-11-1-1-1-111ii−i−i-1-1-1-1-1-1111111-1-1ii−i−i−iiii−i−i−i−iii1-1i−i−i−iii-11
χ1411111111-11-1-1-11111-1-111111-1-11-1-1-1-111ii−i−i-1-1-1-1-1-11111-1-111−i−iii−iiii−i−i−i−iii-11−iiii−i−i1-1
χ1511111111-11-1-1-11111-1-111111-1-11-1-1-1-111−i−iii-1-1-1-1-1-1111111-1-1−i−iiii−i−i−iiiii−i−i1-1−iiii−i−i-11
χ1611111111-11-1-1-11111-1-111111-1-11-1-1-1-111−i−iii-1-1-1-1-1-11111-1-111ii−i−ii−i−i−iiiii−i−i-11i−i−i−iii1-1
χ172222222-22-2222222-2-2-222-2-2-222-22200000000-2-20000000000002222000000000000-2-2000000
χ182222222-22-2222222-2-2-222-2-2-222-22200000000-2-2000000000000-2-2-2-200000000000022000000
χ192222222-2-2-2-2-2-2222-22222-2-2-2-2-2-2-2-200000000220000000000002i2i−2i−2i000000000000−2i2i000000
χ202222222-2-2-2-2-2-2222-22222-2-2-2-2-2-2-2-20000000022000000000000−2i−2i2i2i0000000000002i−2i000000
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
χ22222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-100000000-2-2111111110000000000
χ23222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-11111111100000000-2-2-1-1-1-111110000000000
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
χ25222222-12-22-2-2-2-1-1-12-2-2-1-1-1-1-111-11122-2-22i2i−2i−2i11-1-1-1-11111000000002i−2i−i−iii−i−iii0000000000
χ26222222-12-22-2-2-2-1-1-12-2-2-1-1-1-1-111-11122-2-2−2i−2i2i2i11-1-1-1-1111100000000−2i2iii−i−iii−i−i0000000000
χ27222222-12-22-2-2-2-1-1-12-2-2-1-1-1-1-111-111-2-2222i2i−2i−2i111111-1-1-1-100000000−2i2i−i−iiiii−i−i0000000000
χ28222222-12-22-2-2-2-1-1-12-2-2-1-1-1-1-111-111-2-222−2i−2i2i2i111111-1-1-1-1000000002i−2iii−i−i−i−iii0000000000
χ292222-2-222222-2-2222-2-22-2-22-2-22-222-2000000002-20000000022-2-200000000000000-2200000000
χ302222-2-222222-2-2222-2-22-2-22-2-22-222-2000000002-200000000-2-222000000000000002-200000000
χ312222-2-222-22-222222-22-2-2-22-2-2-222-2200000000-2200000000222200000000000000-2-200000000
χ322222-2-222-22-222222-22-2-2-22-2-2-222-2200000000-2200000000-2-2-2-2000000000000002200000000
χ332222-2-22-22-22-2-222222-2-2-2-2222-2-22-200002i−2i2i−2i-220000000000000000002i−2i2i−2i00000000000000
χ342222-2-22-22-22-2-222222-2-2-2-2222-2-22-20000−2i2i−2i2i-22000000000000000000−2i2i−2i2i00000000000000
χ352222-2-22-2-2-2-2222222-22-2-2-222-22-2-2200002-2-222-20000000000000000002-2-2200000000000000
χ362222-2-22-2-2-2-2222222-22-2-2-222-22-2-220000-222-22-2000000000000000000-222-200000000000000
χ372222-2-2-1-22-22-2-2-1-1-122-2111-1-1-111-1100002i−2i2i−2i1-133−3−333−3−30000000000−ii−ii−i3i3−i3i30000000000
χ382222-2-2-1-22-22-2-2-1-1-122-2111-1-1-111-1100002i−2i2i−2i1-1−3−333−3−3330000000000−ii−iii3−i3i3−i30000000000
χ392222-2-2-1-22-22-2-2-1-1-122-2111-1-1-111-110000−2i2i−2i2i1-133−3−333−3−30000000000i−ii−ii3−i3i3−i30000000000
χ402222-2-2-1-22-22-2-2-1-1-122-2111-1-1-111-110000−2i2i−2i2i1-1−3−333−3−3330000000000i−ii−i−i3i3−i3i30000000000
χ412222-2-2-1-2-2-2-222-1-1-12-22111-1-11-111-100002-2-22-1133−3−3−3−3330000000000-111-1−333−30000000000
χ422222-2-2-1-2-2-2-222-1-1-12-22111-1-11-111-100002-2-22-11−3−33333−3−30000000000-111-13−3−330000000000
χ432222-2-2-1-2-2-2-222-1-1-12-22111-1-11-111-10000-222-2-1133−3−3−3−33300000000001-1-113−3−330000000000
χ442222-2-2-1-2-2-2-222-1-1-12-22111-1-11-111-10000-222-2-11−3−33333−3−300000000001-1-11−333−30000000000
χ452-2-222-22020-22-22-2-20002-2000220-2-22−22−20000002−22−22−22−200002i−2i2i−2i00000000000000−i2i2−i2i200
χ462-2-222-22020-22-22-2-20002-2000220-2-22−22−20000002−22−22−22−20000−2i2i−2i2i00000000000000i2−i2i2−i200
χ472-2-222-22020-22-22-2-20002-2000220-2-2−22−22000000−22−22−22−2200002i−2i2i−2i00000000000000i2−i2i2−i200
χ482-2-222-22020-22-22-2-20002-2000220-2-2−22−22000000−22−22−22−220000−2i2i−2i2i00000000000000−i2i2−i2i200
χ492-2-222-220-202-222-2-20002-2000-2-20222−2−220000002−22−2−22−2200002-2-2200000000000000−222−200
χ502-2-222-220-202-222-2-20002-2000-2-20222−2−220000002−22−2−22−220000-222-2000000000000002−2−2200
χ512-2-222-220-202-222-2-20002-2000-2-2022−222−2000000−22−222−22−200002-2-22000000000000002−2−2200
χ522-2-222-220-202-222-2-20002-2000-2-2022−222−2000000−22−222−22−20000-222-200000000000000−222−200
χ53444444-2-44-4444-2-2-2-4-4-4-2-2222-2-22-2-20000000022000000000000000000000000000000000000
χ54444444-2-4-4-4-4-4-4-2-2-2-444-2-22222222200000000-2-2000000000000000000000000000000000000
χ554444-4-4-24444-4-4-2-2-2-4-4422-222-22-2-2200000000-22000000000000000000000000000000000000
χ564444-4-4-24-44-444-2-2-2-44-422-2222-2-22-2000000002-2000000000000000000000000000000000000
χ5744-4-400440-4000-44-40000040000-4000000000000000000004-400000000000000000000000000
χ5844-4-400440-4000-44-40000040000-400000000000000000000-4400000000000000000000000000
χ5944-4-4004-404000-44-400000-40000400000000000000000000004i−4i000000000000000000000000
χ6044-4-4004-404000-44-400000-4000040000000000000000000000−4i4i000000000000000000000000
χ614-4-444-4-2040-44-4-222000-22000-2-202222−2222−22000000−22−22−22−220000000000000000000000000000
χ624-4-444-4-2040-44-4-222000-22000-2-2022−2222−22220000002−22−22−22−20000000000000000000000000000
χ634-4-444-4-20-404-44-222000-22000220-2-222−22−2222000000−22−222−22−20000000000000000000000000000
χ644-4-444-4-20-404-44-222000-22000220-2-2−222222−220000002−22−2−22−220000000000000000000000000000
χ654-4-44-444040-4-444-4-4000-440004-40-440000000000000000000000000000000000000000000000
χ664-4-44-4440-4044-44-4-4000-44000-4404-40000000000000000000000000000000000000000000000
χ674-4-44-44-2040-4-44-2220002-2000-2202-200000000006−6−666−6−660000000000000000000000000000
χ684-4-44-44-2040-4-44-2220002-2000-2202-20000000000−666−6−666−60000000000000000000000000000
χ694-4-44-44-20-4044-4-2220002-20002-20-2200000000006−6−66−666−60000000000000000000000000000
χ704-4-44-44-20-4044-4-2220002-20002-20-220000000000−666−66−6−660000000000000000000000000000
χ7188-8-800-480-80004-4400000-400004000000000000000000000000000000000000000000000000
χ7288-8-800-4-8080004-440000040000-4000000000000000000000000000000000000000000000000
χ738-88-8008000000-8-8800000000000000000000000000000000000000000000000000000000000
χ748-88-800-400000044-400000043−43000000000000000000000000000000000000000000000000000
χ758-88-800-400000044-4000000−4343000000000000000000000000000000000000000000000000000

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