Finite Group Databasebeta

← Group #10778219

Character table — Group #10778219

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size1111222222222222444444444444488888888888888888812121212121212121616161616161616161624242424242424244848
order1222344444444666244121212121212121212126888888881224242424242424244444888824661212242424242488888824
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ411111111111111111111111111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ5111111111111111111111111111111-1-11111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1
χ6111111111111111111111111111111-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-11111-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111
χ911111-1-1-1-11111111-1-11-1-1-1-1-1-11111-11111-1-1-1-111111-1-1-1-1111111-1-11-111-1-111-1-1-1-11-111-1-1-11
χ1011111-1-1-1-11111111-1-11-1-1-1-1-1-11111-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111-111-1-111-1-111-11-1-1111-1
χ1111111-1-1-1-11111111-1-11-1-1-1-1-1-11111-111-1-111-1-111111-1-1-1-11111-1-111-11-1-111-1-111-1-1-11-1-111-11
χ1211111-1-1-1-11111111-1-11-1-1-1-1-1-11111-111-1-111-1-111111-1-1-1-1-1-1-1-111-1-1-11-1-111-1-111111-111-1-11-1
χ1311111-1-1-1-11111111-1-11-1-1-1-1-1-11111-1-1-111-1-1111-1-1-1-11111111111-1-1-11-1-11111-1-1-1-11-1-1-1111-1
χ1411111-1-1-1-11111111-1-11-1-1-1-1-1-11111-1-1-111-1-1111-1-1-1-11111-1-1-1-1-1-111-11-1-11111-1-111-1111-1-1-11
χ1511111-1-1-1-11111111-1-11-1-1-1-1-1-11111-1-1-1-1-111111-1-1-1-111111111-1-1111-111-1-1-1-111-1-1-1111-1-11-1
χ1611111-1-1-1-11111111-1-11-1-1-1-1-1-11111-1-1-1-1-111111-1-1-1-11111-1-1-1-111-1-11-111-1-1-1-111111-1-1-111-11
χ17222222222-222-2222-2-2-222-2-22222-2-2-200000000-20000000000002222000000000000-2-2000000
χ18222222222-222-2222-2-2-222-2-22222-2-2-200000000-2000000000000-2-2-2-200000000000022000000
χ192222222-2-22-2-222222-2-2-2-2-2-222-2-222200000000-20000000022-2-2000000000000002-200000000
χ202222222-2-22-2-222222-2-2-2-2-2-222-2-222200000000-200000000-2-22200000000000000-2200000000
χ212222222-2-2-2-2-2-2222-222-2-22222-2-2-2-2-2002i−2i2i−2i00200000000000000000000002i−2i2i−2i0000000000
χ222222222-2-2-2-2-2-2222-222-2-22222-2-2-2-2-200−2i2i−2i2i0020000000000000000000000−2i2i−2i2i0000000000
χ2322222-2-2222-2-22222-22-22222-2-2-2-222-200000000-20000000022-2-200000000000000-2200000000
χ2422222-2-2222-2-22222-22-22222-2-2-2-222-200000000-200000000-2-222000000000000002-200000000
χ2522222-2-222-2-2-2-22222-2222-2-2-2-2-2-2-2-22002i−2i−2i2i00200000000000000000000002i−2i−2i2i0000000000
χ2622222-2-222-2-2-2-22222-2222-2-2-2-2-2-2-2-2200−2i2i2i−2i0020000000000000000000000−2i2i2i−2i0000000000
χ2722222-2-2-2-2-222-222222-2-2-222-2-222-2-2200000000-200000000000022-2-2000000000000-22000000
χ2822222-2-2-2-2-222-222222-2-2-222-2-222-2-2200000000-2000000000000-2-2220000000000002-2000000
χ292222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-1-1-10000000000
χ302222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-1-1-1-1-100000000-2-2111111110000000000
χ312222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-11111111100000000-2-21111-1-1-1-10000000000
χ322222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1111111110000000022-1-1-1-111110000000000
χ332222-122-2-2-2-2-2-2-1-1-1-22211-1-1-1-111111002i−2i2i−2i00-133−3−333−3−30000000000−i3i3−i3i3−ii−ii0000000000
χ342222-122-2-2-2-2-2-2-1-1-1-22211-1-1-1-111111002i−2i2i−2i00-1−3−333−3−3330000000000i3−i3i3−i3−ii−ii0000000000
χ352222-122-2-2-2-2-2-2-1-1-1-22211-1-1-1-11111100−2i2i−2i2i00-133−3−333−3−30000000000i3−i3i3−i3i−ii−i0000000000
χ362222-122-2-2-2-2-2-2-1-1-1-22211-1-1-1-11111100−2i2i−2i2i00-1−3−333−3−3330000000000−i3i3−i3i3i−ii−i0000000000
χ372222-1-2-222-2-2-2-2-1-1-12-22-1-111111111-1002i−2i−2i2i00-133−3−3−3−3330000000000−i3i3i3−i3−iii−i0000000000
χ382222-1-2-222-2-2-2-2-1-1-12-22-1-111111111-1002i−2i−2i2i00-1−3−33333−3−30000000000i3−i3−i3i3−iii−i0000000000
χ392222-1-2-222-2-2-2-2-1-1-12-22-1-111111111-100−2i2i2i−2i00-133−3−3−3−3330000000000i3−i3−i3i3i−i−ii0000000000
χ402222-1-2-222-2-2-2-2-1-1-12-22-1-111111111-100−2i2i2i−2i00-1−3−33333−3−30000000000−i3i3i3−i3i−i−ii0000000000
χ412222-1-2-2-2-22222-1-1-1-2-22111111-1-1-1-112222-2-2-2-2-1-1-1-1-11111000000002-2-1-111-1-1110000000000
χ422222-1-2-2-2-22222-1-1-1-2-22111111-1-1-1-1122-2-222-2-2-1-1-1-1-1111100000000-2211-1-111-1-10000000000
χ432222-1-2-2-2-22222-1-1-1-2-22111111-1-1-1-11-2-222-2-222-11111-1-1-1-100000000-2211-1-1-1-1110000000000
χ442222-1-2-2-2-22222-1-1-1-2-22111111-1-1-1-11-2-2-2-22222-11111-1-1-1-1000000002-2-1-11111-1-10000000000
χ4522-2-222i−2i2i−2i02-202-2-20002i−2i002i−2i2-20002−20000−i2i202−22−2−i2i2−i2i200002i−2i2-200000000000000−i2i22−200
χ4622-2-222i−2i2i−2i02-202-2-20002i−2i002i−2i2-20002−20000−i2i202−22−2−i2i2−i2i20000−2i2i-2200000000000000i2−i2−2200
χ4722-2-222i−2i2i−2i02-202-2-20002i−2i002i−2i2-2000−220000i2−i20−22−22i2−i2i2−i200002i−2i2-200000000000000i2−i2−2200
χ4822-2-222i−2i2i−2i02-202-2-20002i−2i002i−2i2-2000−220000i2−i20−22−22i2−i2i2−i20000−2i2i-2200000000000000−i2i22−200
χ4922-2-22−2i2i−2i2i02-202-2-2000−2i2i00−2i2i2-20002−20000i2−i202−22−2i2−i2i2−i200002i−2i-2200000000000000−i2i2−2200
χ5022-2-22−2i2i−2i2i02-202-2-2000−2i2i00−2i2i2-20002−20000i2−i202−22−2i2−i2i2−i20000−2i2i2-200000000000000i2−i22−200
χ5122-2-22−2i2i−2i2i02-202-2-2000−2i2i00−2i2i2-2000−220000−i2i20−22−22−i2i2−i2i200002i−2i-2200000000000000i2−i22−200
χ5222-2-22−2i2i−2i2i02-202-2-2000−2i2i00−2i2i2-2000−220000−i2i20−22−22−i2i2−i2i20000−2i2i2-200000000000000−i2i2−2200
χ534444-24444-444-4-2-2-2-4-4-4-2-222-2-2-2-2222000000002000000000000000000000000000000000000
χ544444-244-4-44-4-44-2-2-24-4-42222-2-222-2-2-2000000002000000000000000000000000000000000000
χ554444-2-4-4444-4-44-2-2-2-44-4-2-2-2-22222-2-22000000002000000000000000000000000000000000000
χ564444-2-4-4-4-4-444-4-2-2-244-422-2-222-2-222-2000000002000000000000000000000000000000000000
χ5744-4-444i−4i−4i4i0-4404-4-4000−4i4i004i−4i-44000000000000000000000000000000000000000000000000
χ5844-4-44−4i4i4i−4i0-4404-4-40004i−4i00−4i4i-44000000000000000000000000000000000000000000000000
χ5944-4-4-24i−4i4i−4i04-40-222000−2i2i00−2i2i-2200022−220000−2i22i20−22−22i2−i2i2−i20000000000000000000000000000
χ6044-4-4-24i−4i4i−4i04-40-222000−2i2i00−2i2i-22000−222200002i2−2i202−22−2−i2i2−i2i20000000000000000000000000000
χ6144-4-4-24i−4i−4i4i0-440-2220002i−2i00−2i2i2-20000000000006−6−66−i6i6i6−i60000000000000000000000000000
χ6244-4-4-24i−4i−4i4i0-440-2220002i−2i00−2i2i2-2000000000000−666−6i6−i6−i6i60000000000000000000000000000
χ6344-4-4-2−4i4i4i−4i0-440-222000−2i2i002i−2i2-20000000000006−6−66i6−i6−i6i60000000000000000000000000000
χ6444-4-4-2−4i4i4i−4i0-440-222000−2i2i002i−2i2-2000000000000−666−6−i6i6i6−i60000000000000000000000000000
χ6544-4-4-2−4i4i−4i4i04-40-2220002i−2i002i−2i-2200022−2200002i2−2i20−22−22−i2i2−i2i20000000000000000000000000000
χ6644-4-4-2−4i4i−4i4i04-40-2220002i−2i002i−2i-22000−22220000−2i22i202−22−2i2−i2i2−i20000000000000000000000000000
χ674-44-440000400-4-4-44000000000004-4000000000000000000004i−4i000000000000000000000000
χ684-44-440000400-4-4-44000000000004-400000000000000000000−4i4i000000000000000000000000
χ694-44-440000-4004-4-4400000000000-440000000000000000004-400000000000000000000000000
χ704-44-440000-4004-4-4400000000000-44000000000000000000-4400000000000000000000000000
χ718-88-8-40000800-844-400000000000-440000000000000000000000000000000000000000000000
χ728-88-8-40000-800844-4000000000004-40000000000000000000000000000000000000000000000
χ738-8-88800000000-88-800000000000000000000000000000000000000000000000000000000000
χ748-8-88-4000000004-440000043−430000000000000000000000000000000000000000000000000000
χ758-8-88-4000000004-4400000−43430000000000000000000000000000000000000000000000000000

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