Finite Group Databasebeta

← Group #10705581

Character table — Group #10705581

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888816161616161616161616161624242424242424242424242424242424
order12222234444666666622444444121212122466661212121212121212444412121212121212128888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i
χ6111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i
χ91111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-11-11-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-11-11-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-1-11-11-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-11-1-11111-1-111-1-1-11-11-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111111-1-1-1-11111111-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-11111111-1-11-1-11111-1-111-1-1-1-11111-1-1-1-111
χ141111111-1-1-1-11111111-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-11111111-1-11-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ151111111-1-1-1-11111111-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-1111111-111-111-1-1-1-11111-1-1-1-111-1-11111-1-1
χ161111111-1-1-1-11111111-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-1111111-111-111-1-1-1-111-1-11111-1-111-1-1-1-111
χ1722222222222222222222-2-2-2-2222222-2-2-2-222-2-2-2-2-2-2220000000000000000000000000000
χ18222222222222222222-2-22222-2-22222-2-2-2-2-2-22222-2-2-2-20000000000000000000000000000
χ192222222-2-2-2-2222222222-2-222-2-2-2-2-2-22-22222-2-222-2-2-2-20000000000000000000000000000
χ202222222-2-2-2-22222222-2-222-2-222-2-2-2-22-222-2-222-2-2-2-2220000000000000000000000000000
χ21222222-12222-1-1-1-1-1-1-122222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ22222222-12222-1-1-1-1-1-1-122222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ23222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-2-211-1-1111111-1-10000−i3i3−i3i3−i3i3−i3i30000000000000000
χ24222222-12222-1-1-1-1-1-1-122-2-2-2-222-1-1-1-1-2-211-1-1111111-1-10000i3−i3i3−i3i3−i3i3−i30000000000000000
χ25222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-2-21111-1-1-1-111110000−i3i3−i3i3i3−i3i3−i30000000000000000
χ26222222-12222-1-1-1-1-1-1-1-2-22222-2-2-1-1-1-1-2-21111-1-1-1-111110000i3−i3i3−i3−i3i3−i3i30000000000000000
χ27222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1111111-1-11122-2-21111-1-1-1-10000000000000000
χ28222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1111111-1-111-2-222-1-1-1-111110000000000000000
χ29222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-21111-2211-1-1-1-111-1-1112-22-2-1-111-1-1110000000000000000
χ30222222-1-2-2-2-2-1-1-1-1-1-1-12222-2-2-2-21111-2211-1-1-1-111-1-111-22-2211-1-111-1-10000000000000000
χ31222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-211112-2-1-1-1-111-1-111110000−i3i3i3−i3−i3i3i3−i30000000000000000
χ32222222-1-2-2-2-2-1-1-1-1-1-1-122-2-222-2-211112-2-1-1-1-111-1-111110000i3−i3−i3i3i3−i3−i3i30000000000000000
χ33222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-22211112-2-1-111-1-11111-1-10000−i3i3i3−i3i3−i3−i3i30000000000000000
χ34222222-1-2-2-2-2-1-1-1-1-1-1-1-2-222-2-22211112-2-1-111-1-11111-1-10000i3−i3−i3i3−i3i3i3−i30000000000000000
χ35222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222221111-22111111-1-1-1-1-1-12-2-2211-1-1-1-1110000000000000000
χ36222222-1-2-2-2-2-1-1-1-1-1-1-1-2-2-2-222221111-22111111-1-1-1-1-1-1-222-2-1-11111-1-10000000000000000
χ372-22-22-222i2i−2i−2i22-2-2-22-2002i−2i2-2002i2i−2i−2i0000002i−2i2-200000000000000002−2−i2i2−i2i22−200000000
χ382-22-22-222i2i−2i−2i22-2-2-22-2002i−2i2-2002i2i−2i−2i0000002i−2i2-20000000000000000−22i2−i2i2−i2−2200000000
χ392-22-22-222i2i−2i−2i22-2-2-22-200−2i2i-22002i2i−2i−2i000000−2i2i-220000000000000000−i2i2−222−2i2−i200000000
χ402-22-22-222i2i−2i−2i22-2-2-22-200−2i2i-22002i2i−2i−2i000000−2i2i-220000000000000000i2−i22−2−22−i2i200000000
χ412-22-22-22−2i−2i2i2i22-2-2-22-2002i−2i-2200−2i−2i2i2i0000002i−2i-220000000000000000−i2i22−2−22i2−i200000000
χ422-22-22-22−2i−2i2i2i22-2-2-22-2002i−2i-2200−2i−2i2i2i0000002i−2i-220000000000000000i2−i2−222−2−i2i200000000
χ432-22-22-22−2i−2i2i2i22-2-2-22-200−2i2i2-200−2i−2i2i2i000000−2i2i2-200000000000000002−2i2−i2i2−i22−200000000
χ442-22-22-22−2i−2i2i2i22-2-2-22-200−2i2i2-200−2i−2i2i2i000000−2i2i2-20000000000000000−22−i2i2−i2i2−2200000000
χ452-22-2-2222i−2i2i−2i-2-222-22-22-200002i−2i2i−2i2i−2i00002-20000002i−2i000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i
χ462-22-2-2222i−2i2i−2i-2-222-22-22-200002i−2i2i−2i2i−2i00002-20000002i−2i00000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i
χ472-22-2-2222i−2i2i−2i-2-222-22-2-220000−2i2i2i−2i2i−2i0000-22000000−2i2i000000000000000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i
χ482-22-2-2222i−2i2i−2i-2-222-22-2-220000−2i2i2i−2i2i−2i0000-22000000−2i2i00000000000000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i
χ492-22-2-222−2i2i−2i2i-2-222-22-22-20000−2i2i−2i2i−2i2i00002-2000000−2i2i000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i
χ502-22-2-222−2i2i−2i2i-2-222-22-22-20000−2i2i−2i2i−2i2i00002-2000000−2i2i00000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i
χ512-22-2-222−2i2i−2i2i-2-222-22-2-2200002i−2i−2i2i−2i2i0000-220000002i−2i000000000000000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i
χ522-22-2-222−2i2i−2i2i-2-222-22-2-2200002i−2i−2i2i−2i2i0000-220000002i−2i00000000000000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i
χ534444-4-444-4-44-4-4-4-4444000000004-4-44000000000000000000000000000000000000000000
χ544444-4-44-444-4-4-4-4-444400000000-444-4000000000000000000000000000000000000000000
χ554444-4-4-24-4-442222-2-2-200000000-222-200−2i32i3000000−2i32i3000000000000000000000000000000
χ564444-4-4-24-4-442222-2-2-200000000-222-2002i3−2i30000002i3−2i3000000000000000000000000000000
χ574444-4-4-2-444-42222-2-2-2000000002-2-2200−2i32i30000002i3−2i3000000000000000000000000000000
χ584444-4-4-2-444-42222-2-2-2000000002-2-22002i3−2i3000000−2i32i3000000000000000000000000000000
χ594-44-44-4-24i4i−4i−4i-2-2222-22004i−4i4-400−2i−2i2i2i000000−2i2i-2200000000000000000000000000000000
χ604-44-44-4-24i4i−4i−4i-2-2222-2200−4i4i-4400−2i−2i2i2i0000002i−2i2-200000000000000000000000000000000
χ614-44-44-4-2−4i−4i4i4i-2-2222-22004i−4i-44002i2i−2i−2i000000−2i2i2-200000000000000000000000000000000
χ624-44-44-4-2−4i−4i4i4i-2-2222-2200−4i4i4-4002i2i−2i−2i0000002i−2i-2200000000000000000000000000000000
χ634-44-4-44-24i−4i4i−4i22-2-22-224-400004i−4i−2i2i−2i2i0000-22000000−2i2i0000000000000000000000000000
χ644-44-4-44-24i−4i4i−4i22-2-22-22-440000−4i4i−2i2i−2i2i00002-20000002i−2i0000000000000000000000000000
χ654-44-4-44-2−4i4i−4i4i22-2-22-224-40000−4i4i2i−2i2i−2i0000-220000002i−2i0000000000000000000000000000
χ664-44-4-44-2−4i4i−4i4i22-2-22-22-4400004i−4i2i−2i2i−2i00002-2000000−2i2i0000000000000000000000000000
χ6788-8-8008000000008-8-8000000000000000000000000000000000000000000000000000000
χ6888-8-800-40000−4i34i3−4i34i3-444000000000000000000000000000000000000000000000000000000
χ6988-8-800-400004i3−4i34i3−4i3-444000000000000000000000000000000000000000000000000000000
χ708-8-8800800000000-8-88000000000000000000000000000000000000000000000000000000
χ718-8-8800-40000−4i34i34i3−4i344-4000000000000000000000000000000000000000000000000000000
χ728-8-8800-400004i3−4i3−4i34i344-4000000000000000000000000000000000000000000000000000000

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