Finite Group Databasebeta

← Group #10778212

Character table — Group #10778212

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222222444444444444488888888888888888812121212121212121616161616161616161624242424242424244848
order122234444444466624466121212121212121288888888121224242424242424244444888824661212242424242488888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-111-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111
χ511111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ611111111111111111111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ711111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-111-1-1
χ811111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111
χ911111-1-1-1-11111111-1-11-1-11-1-1-1-111111-1-111-1-1-111111-1-1-1-1111111-1-11-111-1-111-1-1-1-1111-1-1-11-1
χ1011111-1-1-1-11111111-1-11-1-11-1-1-1-111111-1-111-1-1-111111-1-1-1-1-1-1-1-1-1-1111-111-1-111-1-111-1-1-1111-11
χ1111111-1-1-1-11111111-1-11-1-11-1-1-1-111111-1-1-1-111-11-1-1-1-11111111111-1-1-11-1-11111-1-1-1-1-1-11-111-11
χ1211111-1-1-1-11111111-1-11-1-11-1-1-1-111111-1-1-1-111-11-1-1-1-11111-1-1-1-1-1-111-11-1-11111-1-11111-11-1-11-1
χ1311111-1-1-1-11111111-1-11-1-11-1-1-1-1111-1-11111-1-1-111111-1-1-1-11111-1-111-11-1-111-1-111-1-1-1-1-11111-1
χ1411111-1-1-1-11111111-1-11-1-11-1-1-1-1111-1-11111-1-1-111111-1-1-1-1-1-1-1-111-1-1-11-1-111-1-11111111-1-1-1-11
χ1511111-1-1-1-11111111-1-11-1-11-1-1-1-1111-1-111-1-111-11-1-1-1-111111111-1-1111-111-1-1-1-111-1-111-11-1-1-11
χ1611111-1-1-1-11111111-1-11-1-11-1-1-1-1111-1-111-1-111-11-1-1-1-11111-1-1-1-111-1-11-111-1-1-1-11111-1-11-1111-1
χ17222222222-222-2222-2-2-2-2-2-2222222-200000000-2-2000000000000222200000000000000-2-20000
χ18222222222-222-2222-2-2-2-2-2-2222222-200000000-2-2000000000000-2-2-2-200000000000000220000
χ192222222-2-22-2-222222-2-222222-2-2-2-2200000000-2-20000000022-2-2000000000000002-200000000
χ202222222-2-22-2-222222-2-222222-2-2-2-2200000000-2-200000000-2-22200000000000000-2200000000
χ212222222-2-2-2-2-2-2222-222-2-2-222-2-2-2-2-22i−2i2i−2i00002200000000000000000000002i−2i2i−2i0000000000
χ222222222-2-2-2-2-2-2222-222-2-2-222-2-2-2-2-2−2i2i−2i2i0000220000000000000000000000−2i2i−2i2i0000000000
χ2322222-2-2222-2-22222-22-2-2-22-2-222-2-22000000002-20000000022-2-200000000000000-2200000000
χ2422222-2-2222-2-22222-22-2-2-22-2-222-2-22000000002-200000000-2-222000000000000002-200000000
χ2522222-2-222-2-2-2-22222-2222-2-2-222-2-2-22i−2i−2i2i0000-2200000000000000000000002i−2i−2i2i0000000000
χ2622222-2-222-2-2-2-22222-2222-2-2-222-2-2-2−2i2i2i−2i0000-220000000000000000000000−2i2i2i−2i0000000000
χ2722222-2-2-2-2-222-222222-222-2-2-2-2-222-2000000002-200000000000022-2-200000000000000-220000
χ2822222-2-2-2-2-222-222222-222-2-2-2-2-222-2000000002-2000000000000-2-222000000000000002-20000
χ292222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-1-1-10000000000
χ302222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-11111111100000000-2-21111-1-1-1-10000000000
χ312222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-100000000-2-2111111110000000000
χ322222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000000022-1-1-1-111110000000000
χ332222-122-2-2-2-2-2-2-1-1-1-222111-1-1111112i−2i2i−2i0000-1-133−3−333−3−30000000000−i3i3−i3i3−ii−ii0000000000
χ342222-122-2-2-2-2-2-2-1-1-1-222111-1-1111112i−2i2i−2i0000-1-1−3−333−3−3330000000000i3−i3i3−i3−ii−ii0000000000
χ352222-122-2-2-2-2-2-2-1-1-1-222111-1-111111−2i2i−2i2i0000-1-133−3−333−3−30000000000i3−i3i3−i3i−ii−i0000000000
χ362222-122-2-2-2-2-2-2-1-1-1-222111-1-111111−2i2i−2i2i0000-1-1−3−333−3−3330000000000−i3i3−i3i3i−ii−i0000000000
χ372222-1-2-222-2-2-2-2-1-1-12-22-1-1111-1-11112i−2i−2i2i00001-133−3−3−3−3330000000000−i3i3i3−i3−iii−i0000000000
χ382222-1-2-222-2-2-2-2-1-1-12-22-1-1111-1-11112i−2i−2i2i00001-1−3−33333−3−30000000000i3−i3−i3i3−iii−i0000000000
χ392222-1-2-222-2-2-2-2-1-1-12-22-1-1111-1-1111−2i2i2i−2i00001-133−3−3−3−3330000000000i3−i3−i3i3i−i−ii0000000000
χ402222-1-2-222-2-2-2-2-1-1-12-22-1-1111-1-1111−2i2i2i−2i00001-1−3−33333−3−30000000000−i3i3i3−i3i−i−ii0000000000
χ412222-1-2-2-2-22222-1-1-1-2-2211-11111-1-1-122-2-222-2-21-1-1-1-1-11111000000002-2-1-111-1-1110000000000
χ422222-1-2-2-2-22222-1-1-1-2-2211-11111-1-1-122-2-2-2-2221-11111-1-1-1-100000000-2211-1-1-1-1110000000000
χ432222-1-2-2-2-22222-1-1-1-2-2211-11111-1-1-1-2-22222-2-21-1-1-1-1-1111100000000-2211-1-111-1-10000000000
χ442222-1-2-2-2-22222-1-1-1-2-2211-11111-1-1-1-2-222-2-2221-11111-1-1-1-1000000002-2-1-11111-1-10000000000
χ452-22-222i−2i2i−2i02-202-2-20000002i−2i2i−2i2-200000−i2i22−200−i2i2−i2i22−22−200002-22i−2i000000000000−i2i2002−200
χ462-22-222i−2i2i−2i02-202-2-20000002i−2i2i−2i2-200000−i2i22−200−i2i2−i2i22−22−20000-22−2i2i000000000000i2−i200−2200
χ472-22-222i−2i2i−2i02-202-2-20000002i−2i2i−2i2-200000i2−i2−2200i2−i2i2−i2−22−2200002-22i−2i000000000000i2−i200−2200
χ482-22-222i−2i2i−2i02-202-2-20000002i−2i2i−2i2-200000i2−i2−2200i2−i2i2−i2−22−220000-22−2i2i000000000000−i2i2002−200
χ492-22-22−2i2i−2i2i02-202-2-2000000−2i2i−2i2i2-200000−i2i2−2200−i2i2−i2i2−22−2200002-2−2i2i000000000000−i2i200−2200
χ502-22-22−2i2i−2i2i02-202-2-2000000−2i2i−2i2i2-200000−i2i2−2200−i2i2−i2i2−22−220000-222i−2i000000000000i2−i2002−200
χ512-22-22−2i2i−2i2i02-202-2-2000000−2i2i−2i2i2-200000i2−i22−200i2−i2i2−i22−22−200002-2−2i2i000000000000i2−i2002−200
χ522-22-22−2i2i−2i2i02-202-2-2000000−2i2i−2i2i2-200000i2−i22−200i2−i2i2−i22−22−20000-222i−2i000000000000−i2i200−2200
χ534444-24444-444-4-2-2-2-4-4-4222-2-2-2-2-2-220000000022000000000000000000000000000000000000
χ544444-244-4-44-4-44-2-2-24-4-4-2-2-2-2-22222-20000000022000000000000000000000000000000000000
χ554444-2-4-4444-4-44-2-2-2-44-422-222-2-222-200000000-22000000000000000000000000000000000000
χ564444-2-4-4-4-4-444-4-2-2-244-4-2-222222-2-2200000000-22000000000000000000000000000000000000
χ5744-4-440000400-4-44-4000004000000-40000000000000000004-400000000000000000000000000
χ5844-4-440000400-4-44-4000004000000-4000000000000000000-4400000000000000000000000000
χ5944-4-440000-4004-44-400000-40000004000000000000000000004i−4i000000000000000000000000
χ6044-4-440000-4004-44-400000-4000000400000000000000000000−4i4i000000000000000000000000
χ614-44-444i−4i−4i4i0-4404-4-40000004i−4i−4i4i-4400000000000000000000000000000000000000000000000
χ624-44-44−4i4i4i−4i0-4404-4-4000000−4i4i4i−4i-4400000000000000000000000000000000000000000000000
χ634-44-4-24i−4i4i−4i04-40-222000000−2i2i−2i2i-2200000−2i22i222−2200i2−i2i2−i2−22−220000000000000000000000000000
χ644-44-4-24i−4i4i−4i04-40-222000000−2i2i−2i2i-22000002i2−2i2−222200−i2i2−i2i22−22−20000000000000000000000000000
χ654-44-4-24i−4i−4i4i0-440-222000000−2i2i2i−2i2-200000000000i6−i6−i6i6−666−60000000000000000000000000000
χ664-44-4-24i−4i−4i4i0-440-222000000−2i2i2i−2i2-200000000000−i6i6i6−i66−6−660000000000000000000000000000
χ674-44-4-2−4i4i4i−4i0-440-2220000002i−2i−2i2i2-200000000000i6−i6−i6i66−6−660000000000000000000000000000
χ684-44-4-2−4i4i4i−4i0-440-2220000002i−2i−2i2i2-200000000000−i6i6i6−i6−666−60000000000000000000000000000
χ694-44-4-2−4i4i−4i4i04-40-2220000002i−2i2i−2i-2200000−2i22i2−222200i2−i2i2−i22−22−20000000000000000000000000000
χ704-44-4-2−4i4i−4i4i04-40-2220000002i−2i2i−2i-22000002i2−2i222−2200−i2i2−i2i2−22−220000000000000000000000000000
χ7188-8-8-40000800-84-4400000-400000040000000000000000000000000000000000000000000000
χ7288-8-8-40000-80084-44000004000000-40000000000000000000000000000000000000000000000
χ738-8-88800000000-8-8800000000000000000000000000000000000000000000000000000000000
χ748-8-88-40000000044-4000−4i34i3000000000000000000000000000000000000000000000000000000
χ758-8-88-40000000044-40004i3−4i3000000000000000000000000000000000000000000000000000000

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