Finite Group Databasebeta

← Group #10823076

Character table — Group #10823076

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222222222222244444444444488888888888888888888888888888888888824242424242424242424242424242424
order12222222223444444446666666666612121212121212122222224466666666666688881212121224242424242424244444888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ611111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ711111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ811111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ9111111-1-1-1-111-1-1-1-111111-1-1-1-1111-1-1111-1-1-1-1111-1-11-11-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ10111111-1-1-1-111-1-1-1-111111-1-1-1-1111-1-1111-1-1-1-1111-1-11-11-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ11111111-1-1-1-111-1-1-1-111111-1-1-1-1111-1-1111-1-1-1-1111-1-1-11-111111-1-1-1-1-1-111-1-111-1-111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ12111111-1-1-1-111-1-1-1-111111-1-1-1-1111-1-1111-1-1-1-1111-1-1-11-111111-1-1-1-1-1-111-1-111-1-111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ13111111-1-1-1-111-1-1-1-111111-1-1-1-1111-1-1111-1-1-1-11-1-1111-11-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1
χ14111111-1-1-1-111-1-1-1-111111-1-1-1-1111-1-1111-1-1-1-11-1-1111-11-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111
χ15111111-1-1-1-111-1-1-1-111111-1-1-1-1111-1-1111-1-1-1-11-1-111-11-11-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-111
χ16111111-1-1-1-111-1-1-1-111111-1-1-1-1111-1-1111-1-1-1-11-1-111-11-11-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ1722222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000002i−2i2i−2i0000
χ1822222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000−2i2i−2i2i0000
χ192222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ202222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-11111-2-2-2-21111111111110000000000000000
χ212222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-1-2-2-2-2-1-1-1-1111111110000000000000000
χ222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111122221111-1-1-1-1-1-1-1-10000000000000000
χ23222222-2-2-2-22-22222-2-2-222-2-2-2-2222-2-2-2-2-22222-2000000000000000000000000000000000000000000002i−2i−2i2i0000
χ24222222-2-2-2-22-22222-2-2-222-2-2-2-2222-2-2-2-2-22222-200000000000000000000000000000000000000000000−2i2i2i−2i0000
χ25222222-2-2-2-2-12-2-2-2-2222-1-11111-1-1-111-1-1-11111-122-2-22-22-2-1-1-1-11111-1-11122-2-2-1-111-1-1-1-111110000000000000000
χ26222222-2-2-2-2-12-2-2-2-2222-1-11111-1-1-111-1-1-11111-122-2-2-22-22-1-1-1-1111111-1-1-2-22211-1-11111-1-1-1-10000000000000000
χ27222222-2-2-2-2-12-2-2-2-2222-1-11111-1-1-111-1-1-11111-1-2-2222-22-21111-1-1-1-1-1-111-2-222-1-1111111-1-1-1-10000000000000000
χ28222222-2-2-2-2-12-2-2-2-2222-1-11111-1-1-111-1-1-11111-1-2-222-22-221111-1-1-1-111-1-122-2-211-1-1-1-1-1-111110000000000000000
χ292222-2-222-2-22222-2-2-2-222222222-2-2-2-22-2-222-2-22000022-2-20000000022220000-2-2-2-2000000000000000000000000
χ302222-2-222-2-22222-2-2-2-222222222-2-2-2-22-2-222-2-220000-2-22200000000-2-2-2-200002222000000000000000000000000
χ312222-2-222-2-22-2-2-22222-22222222-2-2-2-2-222-2-222-200000000000000000000000000000000000000002-22-200000000
χ322222-2-222-2-22-2-2-22222-22222222-2-2-2-2-222-2-222-20000000000000000000000000000000000000000-22-2200000000
χ332222-2-222-2-2-1222-2-2-2-22-1-1-1-1-1-1-11111-111-1-111-1000022-2-2−i3−i3i3i3−i3−i3i3i3-1-1-1-100001111−i3−i3i3i3−i3−i3i3i30000000000000000
χ342222-2-222-2-2-1222-2-2-2-22-1-1-1-1-1-1-11111-111-1-111-1000022-2-2i3i3−i3−i3i3i3−i3−i3-1-1-1-100001111i3i3−i3−i3i3i3−i3−i30000000000000000
χ352222-2-222-2-2-1222-2-2-2-22-1-1-1-1-1-1-11111-111-1-111-10000-2-222−i3−i3i3i3−i3−i3i3i311110000-1-1-1-1i3i3−i3−i3i3i3−i3−i30000000000000000
χ362222-2-222-2-2-1222-2-2-2-22-1-1-1-1-1-1-11111-111-1-111-10000-2-222i3i3−i3−i3i3i3−i3−i311110000-1-1-1-1−i3−i3i3i3−i3−i3i3i30000000000000000
χ372222-2-2-2-22222-2-222-2-2222-2-2-2-22-2-2222-2-2-2-222200002-2-220000000022-2-20000-2-222000000000000000000000000
χ382222-2-2-2-22222-2-222-2-2222-2-2-2-22-2-2222-2-2-2-22220000-222-200000000-2-222000022-2-2000000000000000000000000
χ392222-2-2-2-2222-222-2-222-222-2-2-2-22-2-222-22222-2-2-200000000000000000000000000000000000000002-2-2200000000
χ402222-2-2-2-2222-222-2-222-222-2-2-2-22-2-222-22222-2-2-20000000000000000000000000000000000000000-222-200000000
χ412222-2-2-2-222-12-2-222-2-22-1-11111-111-1-1-11111-1-1-100002-2-22−i3−i3i3i3i3i3−i3−i3-1-111000011-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ422222-2-2-2-222-12-2-222-2-22-1-11111-111-1-1-11111-1-1-100002-2-22i3i3−i3−i3−i3−i3i3i3-1-111000011-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
χ432222-2-2-2-222-12-2-222-2-22-1-11111-111-1-1-11111-1-1-10000-222-2−i3−i3i3i3i3i3−i3−i311-1-10000-1-111i3i3−i3−i3−i3−i3i3i30000000000000000
χ442222-2-2-2-222-12-2-222-2-22-1-11111-111-1-1-11111-1-1-10000-222-2i3i3−i3−i3−i3−i3i3i311-1-10000-1-111−i3−i3i3i3i3i3−i3−i30000000000000000
χ4522-2-22-22-22-2222-22-22-2-2-2-222-2-222-22-222-22-22-2-20000000000000000000000000000000000000000000000002i−2i2i−2i
χ4622-2-22-22-22-2222-22-22-2-2-2-222-2-222-22-222-22-22-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i
χ4722-2-22-22-22-22-2-22-22-222-2-222-2-222-22-2-2-22-22-2222-22-200002-22-22-22-2000000000000000000000000000000000000
χ4822-2-22-22-22-22-2-22-22-222-2-222-2-222-22-2-2-22-22-222-22-220000-22-22-22-22000000000000000000000000000000000000
χ4922-2-22-22-22-2-1-2-22-22-22211-1-111-1-11-1111-11-11-1-12-22-20000-11-11-11-11−i3i3−i3i30000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30000000000000000
χ5022-2-22-22-22-2-1-2-22-22-22211-1-111-1-11-1111-11-11-1-12-22-20000-11-11-11-11i3−i3i3−i30000i3−i3i3−i3i3−i3i3−i3i3−i3i3−i30000000000000000
χ5122-2-22-22-22-2-1-2-22-22-22211-1-111-1-11-1111-11-11-1-1-22-2200001-11-11-11-1−i3i3−i3i30000−i3i3−i3i3i3−i3i3−i3i3−i3i3−i30000000000000000
χ5222-2-22-22-22-2-1-2-22-22-22211-1-111-1-11-1111-11-11-1-1-22-2200001-11-11-11-1i3−i3i3−i30000i3−i3i3−i3−i3i3−i3i3−i3i3−i3i30000000000000000
χ5322-2-22-2-22-2222-22-222-2-2-2-2-2-22222-2-2222-2-22-22-20000000000000000000000000000000000000000000000002i−2i−2i2i
χ5422-2-22-2-22-2222-22-222-2-2-2-2-2-22222-2-2222-2-22-22-2000000000000000000000000000000000000000000000000−2i2i2i−2i
χ5522-2-22-2-22-222-22-22-2-222-2-2-2-22222-2-22-2-222-22-222-2-2200002-22-2-22-22000000000000000000000000000000000000
χ5622-2-22-2-22-222-22-22-2-222-2-2-2-22222-2-22-2-222-22-22-222-20000-22-222-22-2000000000000000000000000000000000000
χ5722-2-22-2-22-22-1-22-22-2-2221111-1-1-1-111-111-1-11-11-12-2-220000-11-111-11-1−i3i3i3−i30000−i3i3i3−i3−i3i3−i3i3i3−i3i3−i30000000000000000
χ5822-2-22-2-22-22-1-22-22-2-2221111-1-1-1-111-111-1-11-11-12-2-220000-11-111-11-1i3−i3−i3i30000i3−i3−i3i3i3−i3i3−i3−i3i3−i3i30000000000000000
χ5922-2-22-2-22-22-1-22-22-2-2221111-1-1-1-111-111-1-11-11-1-222-200001-11-1-11-11−i3i3i3−i30000−i3i3i3−i3i3−i3i3−i3−i3i3−i3i30000000000000000
χ6022-2-22-2-22-22-1-22-22-2-2221111-1-1-1-111-111-1-11-11-1-222-200001-11-1-11-11i3−i3−i3i30000i3−i3−i3i3−i3i3−i3i3i3−i3i3−i30000000000000000
χ6122-2-2-222-2-22222-2-22-22-2-2-222-2-22-22-222-222-2-22-20000000000000000000000000000000000002i−2i2i−2i000000000000
χ6222-2-2-222-2-22222-2-22-22-2-2-222-2-22-22-222-222-2-22-2000000000000000000000000000000000000−2i2i−2i2i000000000000
χ6322-2-2-222-2-222-2-222-22-22-2-222-2-22-22-22-22-2-222-22000000000000000000002-22-200002-2-222-2-220000000000000000
χ6422-2-2-222-2-222-2-222-22-22-2-222-2-22-22-22-22-2-222-2200000000000000000000-22-220000-222-2-222-20000000000000000
χ6522-2-2-222-2-22-1-2-222-22-2211-1-111-11-11-11-111-1-11-100000000−i3i3i3−i3−i3i3i3−i3−i3i3−i3i32-22-2i3−i3i3−i3-111-1-111-10000000000000000
χ6622-2-2-222-2-22-1-2-222-22-2211-1-111-11-11-11-111-1-11-100000000−i3i3i3−i3−i3i3i3−i3i3−i3i3−i3-22-22−i3i3−i3i31-1-111-1-110000000000000000
χ6722-2-2-222-2-22-1-2-222-22-2211-1-111-11-11-11-111-1-11-100000000i3−i3−i3i3i3−i3−i3i3−i3i3−i3i3-22-22i3−i3i3−i31-1-111-1-110000000000000000
χ6822-2-2-222-2-22-1-2-222-22-2211-1-111-11-11-11-111-1-11-100000000i3−i3−i3i3i3−i3−i3i3i3−i3i3−i32-22-2−i3i3−i3i3-111-1-111-10000000000000000
χ6922-2-2-22-222-222-222-2-22-2-2-2-2-2222-222-22-22-222-2-20000000000000000000000000000000000002i−2i−2i2i000000000000
χ7022-2-2-22-222-222-222-2-22-2-2-2-2-2222-222-22-22-222-2-2000000000000000000000000000000000000−2i2i2i−2i000000000000
χ7122-2-2-22-222-22-22-2-222-22-2-2-2-2222-222-2-22-22-2-222000000000000000000002-2-2200002-2-22-222-20000000000000000
χ7222-2-2-22-222-22-22-2-222-22-2-2-2-2222-222-2-22-22-2-22200000000000000000000-222-20000-222-22-2-220000000000000000
χ7322-2-2-22-222-2-1-22-2-222-221111-1-1-11-1-111-11-111-1-100000000−i3i3i3−i3i3−i3−i3i3−i3i3i3−i32-2-22i3−i3−i3i3-111-11-1-110000000000000000
χ7422-2-2-22-222-2-1-22-2-222-221111-1-1-11-1-111-11-111-1-100000000−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3-222-2−i3i3i3−i31-1-11-111-10000000000000000
χ7522-2-2-22-222-2-1-22-2-222-221111-1-1-11-1-111-11-111-1-100000000i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3-222-2i3−i3−i3i31-1-11-111-10000000000000000
χ7622-2-2-22-222-2-1-22-2-222-221111-1-1-11-1-111-11-111-1-100000000i3−i3−i3i3−i3i3i3−i3i3−i3−i3i32-2-22−i3i3i3−i3-111-11-1-110000000000000000
χ774444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000000000000000
χ78444444-4-4-4-4-2-44444-4-4-4-2-22222-2-2-222222-2-2-2-220000000000000000000000000000000000000000000000000000
χ794444-4-444-4-4-2-4-4-44444-4-2-2-2-2-2-2-222222-2-222-2-220000000000000000000000000000000000000000000000000000
χ804444-4-4-4-444-2-444-4-444-4-2-22222-222-2-22-2-2-2-22220000000000000000000000000000000000000000000000000000
χ8144-4-44-44-44-4-244-44-44-4-422-2-222-2-22-22-2-22-22-2220000000000000000000000000000000000000000000000000000
χ8244-4-44-4-44-44-24-44-444-4-42222-2-2-2-222-2-2-222-22-220000000000000000000000000000000000000000000000000000
χ8344-4-4-444-4-44-244-4-44-44-422-2-222-22-22-2-22-2-222-220000000000000000000000000000000000000000000000000000
χ8444-4-4-44-444-4-24-444-4-44-42222-2-2-22-2-22-22-22-2-2220000000000000000000000000000000000000000000000000000
χ858-88-80000008000000008-80000-80000000000000000000000000000000000000000000000000000000000000000
χ868-88-8000000-400000000-44−4i34i3−4i34i340000000000000000000000000000000000000000000000000000000000000000
χ878-88-8000000-400000000-444i3−4i34i3−4i340000000000000000000000000000000000000000000000000000000000000000
χ888-8-88000000800000000-880000-80000000000000000000000000000000000000000000000000000000000000000
χ898-8-88000000-4000000004-4−4i34i34i3−4i340000000000000000000000000000000000000000000000000000000000000000
χ908-8-88000000-4000000004-44i3−4i3−4i34i340000000000000000000000000000000000000000000000000000000000000000

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