Finite Group Databasebeta

← Group #10823644

Character table — Group #10823644

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order122222344444444444466612121212661212121212121212121222224444444466666666121212121212121212121212121212122244444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111-1-11-11-1-1-11-11-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111-1-11-11-1-1-11-11-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111111111-1-1-11-11-1-1-11-11-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111-1-1-11-11-1-1-11-11-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ91111111-1-1-1-1-1-1-1-11111111-1-1-1-1111111-1-1-1-1-1-1111-11-1-1-1-11-11111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-1
χ101111111-1-1-1-1-1-1-1-11111111-1-1-1-1111111-1-1-1-1-1-1111-11-1-1-1-11-11111111-1-111-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111
χ111111111-1-1-1-1-1-1-1-11111111-1-1-1-1111111-1-1-1-1-1-111-11-11-1-11-11-11111-1-111-1-111-1-111-1-1-1-111-1-111-1-111-1-1-1-111-1-111
χ121111111-1-1-1-1-1-1-1-11111111-1-1-1-1111111-1-1-1-1-1-111-11-11-1-11-11-11111-1-111-1-111-1-111-1-1-1-111-1-1-1-111-1-11111-1-111-1-1
χ131111111-1-1-1-1-1-1-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-111
χ141111111-1-1-1-1-1-1-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ151111111-1-1-1-1-1-1-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-111-1-11111-1-1
χ161111111-1-1-1-1-1-1-1-11111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-11111-1-111-1-1-1-111
χ1722222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-2222-200002-2000022-2-200000000000022-2-200000000000000000000
χ1822222222222-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-2-2-222-220000-220000-2-222000000000000-2-22200000000000000000000
χ192222222-2-2-2-22222-2-2-2-2222-2-2-2-222-2-2-2-22222-2-22-20000-22000022-2-2000000000000-2-22200000000000000000000
χ202222222-2-2-2-22222-2-2-2-2222-2-2-2-222-2-2-2-22222-2-2-2200002-20000-2-22200000000000022-2-200000000000000000000
χ21222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ22222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222-2-2-2-2-1-1-1-1111111111111-1-1-1-111110000000000000000
χ23222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22-22-2-2-22-22-21111-1-111-1-1-1-111111111-1-1110000000000000000
χ24222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-22-22-2-2-22-22111111-1-11111-1-1-1-1111111-1-10000000000000000
χ25222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-111111111-1-12-200002-20000-1-111−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3-1-111−i3i3−i3i30000000000000000
χ26222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-111111111-1-12-200002-20000-1-111i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3-1-111i3−i3i3−i30000000000000000
χ27222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-111111111-1-1-220000-22000011-1-1−i3i3i3−i3−i3i3−i3i3i3−i3i3−i311-1-1−i3i3i3−i30000000000000000
χ28222222-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-111111111-1-1-220000-22000011-1-1i3−i3−i3i3i3−i3i3−i3−i3i3−i3i311-1-1i3−i3−i3i30000000000000000
χ29222222-1-2-2-2-22222-2-2-2-2-1-1-11111-1-11111-1-1-1-1112-20000-220000-1-111−i3i3i3−i3−i3i3i3−i3−i3i3i3−i311-1-1i3−i3−i3i30000000000000000
χ30222222-1-2-2-2-22222-2-2-2-2-1-1-11111-1-11111-1-1-1-1112-20000-220000-1-111i3−i3−i3i3i3−i3−i3i3i3−i3−i3i311-1-1−i3i3i3−i30000000000000000
χ31222222-1-2-2-2-22222-2-2-2-2-1-1-11111-1-11111-1-1-1-111-2200002-2000011-1-1−i3i3−i3i3−i3i3i3−i3i3−i3−i3i3-1-111i3−i3i3−i30000000000000000
χ32222222-1-2-2-2-22222-2-2-2-2-1-1-11111-1-11111-1-1-1-111-2200002-2000011-1-1i3−i3i3−i3i3−i3−i3i3−i3i3i3−i3-1-111−i3i3−i3i30000000000000000
χ33222222-1-2-2-2-2-2-2-2-22222-1-1-11111-1-1-1-1-1-1111111222-22-2-2-2-22-22-1-1-1-1-1-111-1-111-1-111111111-1-10000000000000000
χ34222222-1-2-2-2-2-2-2-2-22222-1-1-11111-1-1-1-1-1-111111122-22-22-2-22-22-2-1-1-1-111-1-111-1-111-1-11111-1-1110000000000000000
χ35222222-1-2-2-2-2-2-2-2-22222-1-1-11111-1-1-1-1-1-1111111-2-2222222-2-2-2-21111-1-1-1-1-1-11111-1-1-1-1-1-111110000000000000000
χ36222222-1-2-2-2-2-2-2-2-22222-1-1-11111-1-1-1-1-1-1111111-2-2-2-2-2-22222221111111111-1-1-1-111-1-1-1-1-1-1-1-10000000000000000
χ372222-2-2222-2-222-2-222-2-22222222-2-222-2-222-2-2-2-200020-200020-2000000220000-2-2-2-2000000220000000000000000
χ382222-2-2222-2-222-2-222-2-22222222-2-222-2-222-2-2-2-2000-202000-202000000-2-200002222000000-2-20000000000000000
χ392222-2-2222-2-2-2-222-2-2222222222-2-2-2-222-2-222-2-20020-200020-2000002200-2-2-2-20000000022000000000000000000
χ402222-2-2222-2-2-2-222-2-2222222222-2-2-2-222-2-222-2-200-202000-20200000-2-200222200000000-2-2000000000000000000
χ412222-2-22-2-22222-2-2-2-222222-2-2-2-2-2-2-2-22222-2-2220020-2000-202000002200-2-22200000000-2-2000000000000000000
χ422222-2-22-2-22222-2-2-2-222222-2-2-2-2-2-2-2-22222-2-22200-20200020-200000-2-20022-2-20000000022000000000000000000
χ432222-2-22-2-222-2-22222-2-2222-2-2-2-2-2-222-2-2-2-2222200020-2000-20200000022000022-2-2000000-2-20000000000000000
χ442222-2-22-2-222-2-22222-2-2222-2-2-2-2-2-222-2-2-2-22222000-20200020-2000000-2-20000-2-222000000220000000000000000
χ452222-2-2-122-2-222-2-222-2-2-1-1-1-1-1-1-111-1-111-1-1111100020-200020-2−i3i3−i3i3−i3i3-1-1i3−i3i3−i31111−i3i3−i3i3−i3i3-1-10000000000000000
χ462222-2-2-122-2-222-2-222-2-2-1-1-1-1-1-1-111-1-111-1-1111100020-200020-2i3−i3i3−i3i3−i3-1-1−i3i3−i3i31111i3−i3i3−i3i3−i3-1-10000000000000000
χ472222-2-2-122-2-222-2-222-2-2-1-1-1-1-1-1-111-1-111-1-11111000-202000-202−i3i3−i3i3i3−i311−i3i3−i3i3-1-1-1-1−i3i3−i3i3i3−i3110000000000000000
χ482222-2-2-122-2-222-2-222-2-2-1-1-1-1-1-1-111-1-111-1-11111000-202000-202i3−i3i3−i3−i3i311i3−i3i3−i3-1-1-1-1i3−i3i3−i3−i3i3110000000000000000
χ492222-2-2-122-2-2-2-222-2-222-1-1-1-1-1-1-11111-1-111-1-1110020-200020-20−i3i3i3−i3-1-1−i3i31111i3−i3i3−i3−i3i3i3−i3-1-1−i3i30000000000000000
χ502222-2-2-122-2-2-2-222-2-222-1-1-1-1-1-1-11111-1-111-1-1110020-200020-20i3−i3−i3i3-1-1i3−i31111−i3i3−i3i3i3−i3−i3i3-1-1i3−i30000000000000000
χ512222-2-2-122-2-2-2-222-2-222-1-1-1-1-1-1-11111-1-111-1-11100-202000-2020−i3i3i3−i311i3−i3-1-1-1-1−i3i3−i3i3−i3i3i3−i311i3−i30000000000000000
χ522222-2-2-122-2-2-2-222-2-222-1-1-1-1-1-1-11111-1-111-1-11100-202000-2020i3−i3−i3i311−i3i3-1-1-1-1i3−i3i3−i3i3−i3−i3i311−i3i30000000000000000
χ532222-2-2-1-2-22222-2-2-2-222-1-1-111111111-1-1-1-111-1-10020-2000-2020−i3i3i3−i3-1-1i3−i311-1-1i3−i3−i3i3i3−i3−i3i311−i3i30000000000000000
χ542222-2-2-1-2-22222-2-2-2-222-1-1-111111111-1-1-1-111-1-10020-2000-2020i3−i3−i3i3-1-1−i3i311-1-1−i3i3i3−i3−i3i3i3−i311i3−i30000000000000000
χ552222-2-2-1-2-22222-2-2-2-222-1-1-111111111-1-1-1-111-1-100-20200020-20−i3i3i3−i311−i3i3-1-111−i3i3i3−i3i3−i3−i3i3-1-1i3−i30000000000000000
χ562222-2-2-1-2-22222-2-2-2-222-1-1-111111111-1-1-1-111-1-100-20200020-20i3−i3−i3i311i3−i3-1-111i3−i3−i3i3−i3i3i3−i3-1-1−i3i30000000000000000
χ572222-2-2-1-2-222-2-22222-2-2-1-1-1111111-1-11111-1-1-1-100020-2000-202−i3i3−i3i3i3−i3-1-1−i3i3i3−i3-1-111i3−i3i3−i3−i3i3110000000000000000
χ582222-2-2-1-2-222-2-22222-2-2-1-1-1111111-1-11111-1-1-1-100020-2000-202i3−i3i3−i3−i3i3-1-1i3−i3−i3i3-1-111−i3i3−i3i3i3−i3110000000000000000
χ592222-2-2-1-2-222-2-22222-2-2-1-1-1111111-1-11111-1-1-1-1000-20200020-2−i3i3−i3i3−i3i311i3−i3−i3i311-1-1i3−i3i3−i3i3−i3-1-10000000000000000
χ602222-2-2-1-2-222-2-22222-2-2-1-1-1111111-1-11111-1-1-1-1000-20200020-2i3−i3i3−i3i3−i311−i3i3i3−i311-1-1−i3i3−i3i3−i3i3-1-10000000000000000
χ6122-2-22-222i−2i2i−2i2i−2i2i−2i2-22-22-2-22i2i−2i−2i2-22-22-22i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000002i−2i2-2
χ6222-2-22-222i−2i2i−2i2i−2i2i−2i2-22-22-2-22i2i−2i−2i2-22-22-22i−2i2i−2i2i−2i000000000000000000000000000000000000000000000000−2i2i-22
χ6322-2-22-222i−2i2i−2i−2i2i−2i2i-22-222-2-22i2i−2i−2i2-2-22-22−2i2i−2i2i2i−2i000000000000000000000000000000000000000000002-22i−2i0000
χ6422-2-22-222i−2i2i−2i−2i2i−2i2i-22-222-2-22i2i−2i−2i2-2-22-22−2i2i−2i2i2i−2i00000000000000000000000000000000000000000000-22−2i2i0000
χ6522-2-22-22−2i2i−2i2i2i−2i2i−2i-22-222-2-2−2i−2i2i2i2-2-22-222i−2i2i−2i−2i2i000000000000000000000000000000000000000000002-2−2i2i0000
χ6622-2-22-22−2i2i−2i2i2i−2i2i−2i-22-222-2-2−2i−2i2i2i2-2-22-222i−2i2i−2i−2i2i00000000000000000000000000000000000000000000-222i−2i0000
χ6722-2-22-22−2i2i−2i2i−2i2i−2i2i2-22-22-2-2−2i−2i2i2i2-22-22-2−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000002i−2i-22
χ6822-2-22-22−2i2i−2i2i−2i2i−2i2i2-22-22-2-2−2i−2i2i2i2-22-22-2−2i2i−2i2i−2i2i000000000000000000000000000000000000000000000000−2i2i2-2
χ6922-2-2-2222i−2i−2i2i2i−2i−2i2i2-2-222-2-22i2i−2i−2i-222-2-222i−2i−2i2i−2i2i0000000000000000000000000000000000002-22i−2i000000000000
χ7022-2-2-2222i−2i−2i2i2i−2i−2i2i2-2-222-2-22i2i−2i−2i-222-2-222i−2i−2i2i−2i2i000000000000000000000000000000000000-22−2i2i000000000000
χ7122-2-2-2222i−2i−2i2i−2i2i2i−2i-222-22-2-22i2i−2i−2i-22-222-2−2i2i2i−2i−2i2i00000000000000000000000000000000000000002-22i−2i00000000
χ7222-2-2-2222i−2i−2i2i−2i2i2i−2i-222-22-2-22i2i−2i−2i-22-222-2−2i2i2i−2i−2i2i0000000000000000000000000000000000000000-22−2i2i00000000
χ7322-2-2-222−2i2i2i−2i2i−2i−2i2i-222-22-2-2−2i−2i2i2i-22-222-22i−2i−2i2i2i−2i00000000000000000000000000000000000000002-2−2i2i00000000
χ7422-2-2-222−2i2i2i−2i2i−2i−2i2i-222-22-2-2−2i−2i2i2i-22-222-22i−2i−2i2i2i−2i0000000000000000000000000000000000000000-222i−2i00000000
χ7522-2-2-222−2i2i2i−2i−2i2i2i−2i2-2-222-2-2−2i−2i2i2i-222-2-22−2i2i2i−2i2i−2i0000000000000000000000000000000000002-2−2i2i000000000000
χ7622-2-2-222−2i2i2i−2i−2i2i2i−2i2-2-222-2-2−2i−2i2i2i-222-2-22−2i2i2i−2i2i−2i000000000000000000000000000000000000-222i−2i000000000000
χ7744-4-44-4-24i−4i4i−4i4i−4i4i−4i4-44-4-222−2i−2i2i2i-22-22-22−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ7844-4-44-4-24i−4i4i−4i−4i4i−4i4i-44-44-222−2i−2i2i2i-222-22-22i−2i2i−2i−2i2i0000000000000000000000000000000000000000000000000000
χ7944-4-44-4-2−4i4i−4i4i4i−4i4i−4i-44-44-2222i2i−2i−2i-222-22-2−2i2i−2i2i2i−2i0000000000000000000000000000000000000000000000000000
χ8044-4-44-4-2−4i4i−4i4i−4i4i−4i4i4-44-4-2222i2i−2i−2i-22-22-222i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ8144-4-4-44-24i−4i−4i4i4i−4i−4i4i4-4-44-222−2i−2i2i2i2-2-222-2−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000
χ8244-4-4-44-24i−4i−4i4i−4i4i4i−4i-444-4-222−2i−2i2i2i2-22-2-222i−2i−2i2i2i−2i0000000000000000000000000000000000000000000000000000
χ8344-4-4-44-2−4i4i4i−4i4i−4i−4i4i-444-4-2222i2i−2i−2i2-22-2-22−2i2i2i−2i−2i2i0000000000000000000000000000000000000000000000000000
χ8444-4-4-44-2−4i4i4i−4i−4i4i4i−4i4-4-44-2222i2i−2i−2i2-2-222-22i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000
χ858-88-8008000000000000-8-8800000000000000000000000000000000000000000000000000000000000000000000
χ868-88-800-400000000000044-4−4i34i3−4i34i30000000000000000000000000000000000000000000000000000000000000000
χ878-88-800-400000000000044-44i3−4i34i3−4i30000000000000000000000000000000000000000000000000000000000000000
χ888-8-88008000000000000-88-800000000000000000000000000000000000000000000000000000000000000000000
χ898-8-8800-40000000000004-4443−43−43430000000000000000000000000000000000000000000000000000000000000000
χ908-8-8800-40000000000004-44−434343−430000000000000000000000000000000000000000000000000000000000000000

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