Finite Group Databasebeta

← Group #10831848

Character table — Group #10831848

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222222222222224444444444444444444444448888888888888888888888888888888812121212121212122424242448484848
order122222222234444666224444666666666612121212121212124444444444121212121212121212121212121212121212121212122222444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-111-1-1
χ6111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-111-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-111-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-111-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ911111111111-1-1-1-11111111-1-111111111111111-1-1-1-1-11-11-1-11-11-1-1-111-1-111-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-11-11-1
χ1011111111111-1-1-1-11111111-1-111111111111111-1-1-1-1-11-11-1-11-11-1-1-111-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-111-11-11
χ1111111111111-1-1-1-11111111-1-111111111111111-1-1-1-1-1-11-11-1-11-11-1-1-1-111-1-111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-11-11
χ1211111111111-1-1-1-11111111-1-111111111111111-1-1-1-1-1-11-11-1-11-11-1-1-1-111-1-111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1111-11-1
χ1311111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-111111-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-1-1-1111-1-11
χ1411111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1111111-1-1-111-1
χ1511111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-111-11-111-111-1-11111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-111-111-1
χ1611111111111-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-111-11-111-111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1111111-1-11-1-11
χ172222222222-12222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ182222222222-12222-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2-2-22-2-2-2-2-1-111111111-1-1-1-1111111110000000000000000
χ192222222222-12222-1-1-1-2-2-2-222-1-1-1-1-1-111111111-1-1-1-1-222-2-2-222-2-211-1-1-1-11111-1-111-1-1-1-111110000000000000000
χ202222222222-12222-1-1-1-2-2-2-222-1-1-1-1-1-111111111-1-1-1-1-2-2-222-2-2-222111111-1-1-1-1-1-1111111-1-1-1-10000000000000000
χ212222222222-1-2-2-2-2-1-1-12222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-22-22-2-22-22-211-1-111-1-1111111-1-111-1-1110000000000000000
χ222222222222-1-2-2-2-2-1-1-12222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-2-22-22-2-22-221111-1-111-1-1111111-1-111-1-10000000000000000
χ232222222222-1-2-2-2-2-1-1-1-2-2-2-2-2-2-1-1-1-1-1-111111111111122-2-2222-2-22-1-1-1-11111-1-111-1-1-1-11111-1-10000000000000000
χ242222222222-1-2-2-2-2-1-1-1-2-2-2-2-2-2-1-1-1-1-1-11111111111112-222-22-222-2-1-111-1-1-1-11111-1-111-1-1-1-1110000000000000000
χ2522222-2-2-22-2222-2-222200002-222-2-2-2-20000000022-2-200022000-2-200000022222-2000000-2-2-2-20000000000000000
χ2622222-2-2-22-2222-2-222200002-222-2-2-2-20000000022-2-2000-2-200022000000-2-2-2-22-200000022220000000000000000
χ2722222-2-2-22-22-2-2222220000-2222-2-2-2-200000000-2-2220002-2000-2200000022-2-2-22000000-2-2220000000000000000
χ2822222-2-2-22-22-2-2222220000-2222-2-2-2-200000000-2-222000-220002-2000000-2-222-2200000022-2-20000000000000000
χ2922222-2-2-22-2-122-2-2-1-1-100002-2-1-11111−i3−i3i3i3−i3−i3i3i3-1-11100022000-2-2−i3i3−i3i3−i3i3-1-1-1-1-11−i3i3−i3i3−i3i311110000000000000000
χ3022222-2-2-22-2-122-2-2-1-1-100002-2-1-11111−i3−i3i3i3−i3−i3i3i3-1-111000-2-200022−i3i3i3−i3i3−i31111-11−i3i3i3−i3i3−i3-1-1-1-10000000000000000
χ3122222-2-2-22-2-122-2-2-1-1-100002-2-1-11111i3i3−i3−i3i3i3−i3−i3-1-11100022000-2-2i3−i3i3−i3i3−i3-1-1-1-1-11i3−i3i3−i3i3−i311110000000000000000
χ3222222-2-2-22-2-122-2-2-1-1-100002-2-1-11111i3i3−i3−i3i3i3−i3−i3-1-111000-2-200022i3−i3−i3i3−i3i31111-11i3−i3−i3i3−i3i3-1-1-1-10000000000000000
χ3322222-2-2-22-2-1-2-222-1-1-10000-22-1-11111−i3−i3i3i3−i3−i3i3i311-1-10002-2000-22i3−i3−i3i3i3−i3-1-1111-1i3−i3−i3i3i3−i311-1-10000000000000000
χ3422222-2-2-22-2-1-2-222-1-1-10000-22-1-11111−i3−i3i3i3−i3−i3i3i311-1-1000-220002-2i3−i3i3−i3−i3i311-1-11-1i3−i3i3−i3−i3i3-1-1110000000000000000
χ3522222-2-2-22-2-1-2-222-1-1-10000-22-1-11111i3i3−i3−i3i3i3−i3−i311-1-10002-2000-22−i3i3i3−i3−i3i3-1-1111-1−i3i3i3−i3−i3i311-1-10000000000000000
χ3622222-2-2-22-2-1-2-222-1-1-10000-22-1-11111i3i3−i3−i3i3i3−i3−i311-1-1000-220002-2−i3i3−i3i3i3−i311-1-11-1−i3i3−i3i3i3−i3-1-1110000000000000000
χ372222-22-2-2-22222-2-22220000-22-2-222-2-20000000022-2-2022000-2-2000022220000-2200-2-2-2-200000000000000000000
χ382222-22-2-2-22222-2-22220000-22-2-222-2-20000000022-2-20-2-2000220000-2-2-2-20000-2200222200000000000000000000
χ392222-22-2-2-222-2-22222200002-2-2-222-2-200000000-2-22202-2000-22000022-2-200002-200-2-22200000000000000000000
χ402222-22-2-2-222-2-22222200002-2-2-222-2-200000000-2-2220-220002-20000-2-22200002-20022-2-200000000000000000000
χ412222-22-2-2-22-122-2-2-1-1-10000-2211-1-111−i3−i3i3i3i3i3−i3−i3-1-111022000-2-200i3−i3-1-1-1-1−i3i3−i3i31-1−i3i31111−i3i3−i3i30000000000000000
χ422222-22-2-2-22-122-2-2-1-1-10000-2211-1-111−i3−i3i3i3i3i3−i3−i3-1-1110-2-20002200i3−i31111i3−i3i3−i31-1−i3i3-1-1-1-1i3−i3i3−i30000000000000000
χ432222-22-2-2-22-122-2-2-1-1-10000-2211-1-111i3i3−i3−i3−i3−i3i3i3-1-111022000-2-200−i3i3-1-1-1-1i3−i3i3−i31-1i3−i31111i3−i3i3−i30000000000000000
χ442222-22-2-2-22-122-2-2-1-1-10000-2211-1-111i3i3−i3−i3−i3−i3i3i3-1-1110-2-20002200−i3i31111−i3i3−i3i31-1i3−i3-1-1-1-1−i3i3−i3i30000000000000000
χ452222-22-2-2-22-1-2-222-1-1-100002-211-1-111−i3−i3i3i3i3i3−i3−i311-1-102-2000-2200−i3i3-1-111−i3i3i3−i3-11i3−i311-1-1−i3i3i3−i30000000000000000
χ462222-22-2-2-22-1-2-222-1-1-100002-211-1-111−i3−i3i3i3i3i3−i3−i311-1-10-220002-200−i3i311-1-1i3−i3−i3i3-11i3−i3-1-111i3−i3−i3i30000000000000000
χ472222-22-2-2-22-1-2-222-1-1-100002-211-1-111i3i3−i3−i3−i3−i3i3i311-1-102-2000-2200i3−i3-1-111i3−i3−i3i3-11−i3i311-1-1i3−i3−i3i30000000000000000
χ482222-22-2-2-22-1-2-222-1-1-100002-211-1-111i3i3−i3−i3−i3−i3i3i311-1-10-220002-200i3−i311-1-1−i3i3i3−i3-11−i3i3-1-111−i3i3i3−i30000000000000000
χ492222-2-222-2-22222222222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2000020000-2-200000000-2-222000000000000000000000000
χ502222-2-222-2-222222222-2-222-2-2-2-2-2-222-2-2-2-22222222220000-200002200000000-2-2-2-2000000000000000000000000
χ512222-2-222-2-22-2-2-2-222222-2-222-2-2-2-2222222-2-2-2-2-2-2-2-220000-20000220000000022-2-2000000000000000000000000
χ522222-2-222-2-22-2-2-2-2222-2-22222-2-2-2-222-2-2-2-22222-2-2-2-2-2000020000-2-2000000002222000000000000000000000000
χ532222-2-222-2-2-12222-1-1-122-2-2-2-21111-1-1-1-1-1-11111-1-1-1-1-200002000011−i3i3−i3i3−i3i3−i3i311-1-1i3−i3i3−i3i3−i3i3−i30000000000000000
χ542222-2-222-2-2-12222-1-1-122-2-2-2-21111-1-1-1-1-1-11111-1-1-1-1-200002000011i3−i3i3−i3i3−i3i3−i311-1-1−i3i3−i3i3−i3i3−i3i30000000000000000
χ552222-2-222-2-2-12222-1-1-1-2-222-2-21111-1-11111-1-1-1-1-1-1-1-120000-20000-1-1−i3i3−i3i3i3−i3i3−i31111i3−i3i3−i3−i3i3−i3i30000000000000000
χ562222-2-222-2-2-12222-1-1-1-2-222-2-21111-1-11111-1-1-1-1-1-1-1-120000-20000-1-1i3−i3i3−i3−i3i3−i3i31111−i3i3−i3i3i3−i3i3−i30000000000000000
χ572222-2-222-2-2-1-2-2-2-2-1-1-122-2-2221111-1-1-1-1-1-11111111120000-20000-1-1−i3i3i3−i3−i3i3i3−i3-1-111i3−i3−i3i3i3−i3−i3i30000000000000000
χ582222-2-222-2-2-1-2-2-2-2-1-1-122-2-2221111-1-1-1-1-1-11111111120000-20000-1-1i3−i3−i3i3i3−i3−i3i3-1-111−i3i3i3−i3−i3i3i3−i30000000000000000
χ592222-2-222-2-2-1-2-2-2-2-1-1-1-2-222221111-1-11111-1-1-1-11111-200002000011−i3i3i3−i3i3−i3−i3i3-1-1-1-1i3−i3−i3i3−i3i3i3−i30000000000000000
χ602222-2-222-2-2-1-2-2-2-2-1-1-1-2-222221111-1-11111-1-1-1-11111-200002000011i3−i3−i3i3−i3i3i3−i3-1-1-1-1−i3i3i3−i3i3−i3−i3i30000000000000000
χ6122-2-2222-2-2-2200002-2-22-22-2002-22-22-22-22-22-22-200000000000000000000000000000000000022-2-200002-2000000
χ6222-2-2222-2-2-2200002-2-22-22-2002-22-22-22-22-22-22-2000000000000000000000000000000000000-2-2220000-22000000
χ6322-2-2222-2-2-2200002-2-2-22-22002-22-22-2-22-22-22-2200000000000000000000000000000000000022-2-20000-22000000
χ6422-2-2222-2-2-2200002-2-2-22-22002-22-22-2-22-22-22-22000000000000000000000000000000000000-2-22200002-2000000
χ6522-2-2-2-22-222200002-2-22-2-2200-22-222-22-22-2-22-2200000000000000000000000000000000000000002i2i−2i−2i002i−2i0000
χ6622-2-2-2-22-222200002-2-22-2-2200-22-222-22-22-2-22-220000000000000000000000000000000000000000−2i−2i2i2i00−2i2i0000
χ6722-2-2-2-22-222200002-2-2-222-200-22-222-2-22-222-22-200000000000000000000000000000000000000002i2i−2i−2i00−2i2i0000
χ6822-2-2-2-22-222200002-2-2-222-200-22-222-2-22-222-22-20000000000000000000000000000000000000000−2i−2i2i2i002i−2i0000
χ6944-4-4444-4-4-4-20000-2224-44-400-22-22-22-22-22-22-220000000000000000000000000000000000000000000000000000
χ7044-4-4444-4-4-4-20000-222-44-4400-22-22-222-22-22-22-20000000000000000000000000000000000000000000000000000
χ7144-4-44-4-44-44400004-4-40000004-4-44-44000000000000000000000000000000000000000000000000000000000000
χ7244-4-44-4-44-44-20000-222000000-222-22-2−2i32i32i3−2i3−2i32i32i3−2i30000000000000000000000000000000000000000000000000000
χ7344-4-44-4-44-44-20000-222000000-222-22-22i3−2i3−2i32i32i3−2i3−2i32i30000000000000000000000000000000000000000000000000000
χ7444-4-4-44-444-4400004-4-4000000-444-4-44000000000000000000000000000000000000000000000000000000000000
χ7544-4-4-44-444-4-20000-2220000002-2-222-2−2i32i32i3−2i32i3−2i3−2i32i30000000000000000000000000000000000000000000000000000
χ7644-4-4-44-444-4-20000-2220000002-2-222-22i3−2i3−2i32i3−2i32i32i3−2i30000000000000000000000000000000000000000000000000000
χ7744-4-4-4-44-444-20000-2224-4-44002-22-2-22-22-222-22-20000000000000000000000000000000000000000000000000000
χ7844-4-4-4-44-444-20000-222-444-4002-22-2-222-22-2-22-220000000000000000000000000000000000000000000000000000
χ794-44-40000004004i−4i-44-400000000000000000000004i−4i000000000000000000000000000000002-22-22i−2i2i−2i00000000
χ804-44-40000004004i−4i-44-400000000000000000000004i−4i00000000000000000000000000000000-22-22−2i2i−2i2i00000000
χ814-44-4000000400−4i4i-44-40000000000000000000000−4i4i000000000000000000000000000000002-22-2−2i2i−2i2i00000000
χ824-44-4000000400−4i4i-44-40000000000000000000000−4i4i00000000000000000000000000000000-22-222i−2i2i−2i00000000
χ834-4-4400000044-400-4-44000000000000000000004-400000000000000000000000000000000002-2-222-2-2200000000
χ844-4-4400000044-400-4-44000000000000000000004-40000000000000000000000000000000000-222-2-222-200000000
χ854-4-440000004-4400-4-4400000000000000000000-4400000000000000000000000000000000002-2-22-222-200000000
χ864-4-440000004-4400-4-4400000000000000000000-440000000000000000000000000000000000-222-22-2-2200000000
χ878-88-8000000-4008i−8i4-440000000000000000000000−4i4i000000000000000000000000000000000000000000000000
χ888-88-8000000-400−8i8i4-4400000000000000000000004i−4i000000000000000000000000000000000000000000000000
χ898-8-88000000-48-80044-400000000000000000000-4400000000000000000000000000000000000000000000000000
χ908-8-88000000-4-880044-4000000000000000000004-400000000000000000000000000000000000000000000000000

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