Finite Group Databasebeta

← Group #10823688

Character table — Group #10823688

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order1222444422222234444446661212121266666612121212121222244444444466666612121212121212121212121212121212121222224444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-111-1-1-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111-1-111-1-1-1-11-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-11-1-1-111-1-1-11-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111-11-1-1-111-1-1-11-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111111111111111111111-1-11-1-1-1-111-1-11-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-11-1-1-1-111-1-11-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-111-11-11-11-1-1-111111-1-111-1-111-1-111-1-1-1-1-1-1111111-1-1-1-111-1-111-1-111-1-1
χ101111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-111-11-11-11-1-1-111111-1-111-1-111-1-111-1-1-1-1-1-111-1-1-1-11111-1-111-1-111-1-111
χ111111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-11-111-1-11-11-11-111-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-111-1-1-1-111-1-111
χ121111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-11-111-1-11-11-11-111-1-11111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-11111-1-111-1-1
χ131111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-111-111-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ141111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-111-111-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ151111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-111-1111-1-1-1-1-1-1-1-111-1-11111-1-11111111111-1-1-1-1-1-111-1-11111-1-1
χ161111-1-1-1-11111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-111-1111-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-1111111-1-111-1-1-1-111
χ1722222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ1822222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-222-2-2-2-22-2-2-1-11111-1-1-1-111111111-1-1111100000000000000000000
χ1922222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-22-2-2-222-2-2-22-211-1-1111111-1-1-1-1111111-1-11100000000000000000000
χ2022222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22-2-2-2-222-2-221111-1-111111111-1-1-1-11111-1-100000000000000000000
χ212222222222-2-2-2-2222-2-2-2-2222222222-2-2-2-222-2-2-2-20020000-2-200200002200000000-2-2-2-200002200000000000000000000
χ222222222222-2-2-2-2222-2-2-2-2222222222-2-2-2-222-2-2-2-200-200002200-20000-2-20000000022220000-2-200000000000000000000
χ232222222222-2-2-2-2-122-2-2-2-2-1-1-1-1-1-1-1-1-11111-1-111110020000-2-2002−i3i3−i3i3-1-1−i3i3−i3i3−i3i3−i3i31111−i3i3−i3i3-1-100000000000000000000
χ242222222222-2-2-2-2-122-2-2-2-2-1-1-1-1-1-1-1-1-11111-1-111110020000-2-2002i3−i3i3−i3-1-1i3−i3i3−i3i3−i3i3−i31111i3−i3i3−i3-1-100000000000000000000
χ252222222222-2-2-2-2-122-2-2-2-2-1-1-1-1-1-1-1-1-11111-1-1111100-200002200-2−i3i3i3−i311−i3i3−i3i3i3−i3i3−i3-1-1-1-1−i3i3i3−i31100000000000000000000
χ262222222222-2-2-2-2-122-2-2-2-2-1-1-1-1-1-1-1-1-11111-1-1111100-200002200-2i3−i3−i3i311i3−i3i3−i3−i3i3−i3i3-1-1-1-1i3−i3−i3i31100000000000000000000
χ2722222222-2-222-2-22-2-222-2-22222222-2-222-2-2-2-222-2-202000-2-2000200022000000-2-2-2-2000000220000000000000000000000
χ2822222222-2-222-2-22-2-222-2-22222222-2-222-2-2-2-222-2-20-200022000-2000-2-20000002222000000-2-20000000000000000000000
χ2922222222-2-222-2-2-1-2-222-2-2-1-1-1-1-1-1-111-1-11111-1-11102000-2-200020−i3i3-1-1−i3i3i3−i3i3−i31111−i3i3−i3i3−i3i3-1-1−i3i300000000000000000000
χ3022222222-2-222-2-2-1-2-222-2-2-1-1-1-1-1-1-111-1-11111-1-11102000-2-200020i3−i3-1-1i3−i3−i3i3−i3i31111i3−i3i3−i3i3−i3-1-1i3−i300000000000000000000
χ3122222222-2-222-2-2-1-2-222-2-2-1-1-1-1-1-1-111-1-11111-1-1110-200022000-20−i3i311i3−i3i3−i3i3−i3-1-1-1-1i3−i3i3−i3−i3i311i3−i300000000000000000000
χ3222222222-2-222-2-2-1-2-222-2-2-1-1-1-1-1-1-111-1-11111-1-1110-200022000-20i3−i311−i3i3−i3i3−i3i3-1-1-1-1−i3i3−i3i3i3−i311−i3i300000000000000000000
χ3322222222-2-2-2-2222-2-2-2-2222222222-2-2-2-222-2-2-2-222200-2-20000200220000-2-2-2-20000000022000000000000000000000000
χ3422222222-2-2-2-2222-2-2-2-2222222222-2-2-2-222-2-2-2-222-200220000-200-2-20000222200000000-2-2000000000000000000000000
χ3522222222-2-2-2-222-1-2-2-2-222-1-1-1-1-1-1-11111-1-11111-1-1200-2-20000200-1-1−i3i3−i3i31111i3−i3i3−i3i3−i3i3−i3-1-1−i3i3−i3i300000000000000000000
χ3622222222-2-2-2-222-1-2-2-2-222-1-1-1-1-1-1-11111-1-11111-1-1200-2-20000200-1-1i3−i3i3−i31111−i3i3−i3i3−i3i3−i3i3-1-1i3−i3i3−i300000000000000000000
χ3722222222-2-2-2-222-1-2-2-2-222-1-1-1-1-1-1-11111-1-11111-1-1-200220000-20011−i3i3i3−i3-1-1-1-1i3−i3i3−i3−i3i3−i3i311−i3i3i3−i300000000000000000000
χ3822222222-2-2-2-222-1-2-2-2-222-1-1-1-1-1-1-11111-1-11111-1-1-200220000-20011i3−i3−i3i3-1-1-1-1−i3i3−i3i3i3−i3i3−i311i3−i3−i3i300000000000000000000
χ392222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-111111122-22-22-22-2-2-22-1-1-1-111-1-111-1-111-1-1111111-1-100000000000000000000
χ402222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-11111112-222-2-22-22-22-2-1-111-1-1-1-11111-1-111-1-111-1-11100000000000000000000
χ412222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-1111111-222-222-2-222-2-211-1-1-1-111-1-1-1-11111-1-1-1-1111100000000000000000000
χ422222-2-2-2-2222222-1-2-2-2-2-2-2-1-1-11111-1-1-1-1-1-1111111-2-2-2-22-222-222211111111-1-111-1-1-1-111-1-1-1-1-1-100000000000000000000
χ432222-2-2-2-222-2-2-2-22-2-22222222-2-2-2-222-2-2-2-2-2-2222200200002-200-20000220000000022-2-20000-2-200000000000000000000
χ442222-2-2-2-222-2-2-2-22-2-22222222-2-2-2-222-2-2-2-2-2-2222200-20000-220020000-2-200000000-2-22200002200000000000000000000
χ452222-2-2-2-222-2-2-2-2-1-2-22222-1-1-11111-1-1111111-1-1-1-100200002-200-2−i3i3i3−i3-1-1−i3i3i3−i3i3−i3−i3i3-1-111i3−i3−i3i31100000000000000000000
χ462222-2-2-2-222-2-2-2-2-1-2-22222-1-1-11111-1-1111111-1-1-1-100200002-200-2i3−i3−i3i3-1-1i3−i3−i3i3−i3i3i3−i3-1-111−i3i3i3−i31100000000000000000000
χ472222-2-2-2-222-2-2-2-2-1-2-22222-1-1-11111-1-1111111-1-1-1-100-20000-22002−i3i3−i3i311−i3i3i3−i3−i3i3i3−i311-1-1i3−i3i3−i3-1-100000000000000000000
χ482222-2-2-2-222-2-2-2-2-1-2-22222-1-1-11111-1-1111111-1-1-1-100-20000-22002i3−i3i3−i311i3−i3−i3i3i3−i3−i3i311-1-1−i3i3−i3i3-1-100000000000000000000
χ492222-2-2-2-2-2-222-2-2222-2-222222-2-2-2-2-2-222-2-222-2-22202000-22000-200022000000-2-222000000-2-20000000000000000000000
χ502222-2-2-2-2-2-222-2-2222-2-222222-2-2-2-2-2-222-2-222-2-2220-20002-20002000-2-200000022-2-2000000220000000000000000000000
χ512222-2-2-2-2-2-222-2-2-122-2-222-1-1-1111111-1-111-1-111-1-102000-22000-20−i3i3-1-1i3−i3i3−i3−i3i311-1-1−i3i3i3−i3i3−i311−i3i300000000000000000000
χ522222-2-2-2-2-2-222-2-2-122-2-222-1-1-1111111-1-111-1-111-1-102000-22000-20i3−i3-1-1−i3i3−i3i3i3−i311-1-1i3−i3−i3i3−i3i311i3−i300000000000000000000
χ532222-2-2-2-2-2-222-2-2-122-2-222-1-1-1111111-1-111-1-111-1-10-20002-200020−i3i311−i3i3i3−i3−i3i3-1-111i3−i3−i3i3i3−i3-1-1i3−i300000000000000000000
χ542222-2-2-2-2-2-222-2-2-122-2-222-1-1-1111111-1-111-1-111-1-10-20002-200020i3−i311i3−i3−i3i3i3−i3-1-111−i3i3i3−i3−i3i3-1-1−i3i300000000000000000000
χ552222-2-2-2-2-2-2-2-22222222-2-2222-2-2-2-2-2-2-2-2222222-2-2200-220000-200220000-2-22200000000-2-2000000000000000000000000
χ562222-2-2-2-2-2-2-2-22222222-2-2222-2-2-2-2-2-2-2-2222222-2-2-2002-20000200-2-2000022-2-20000000022000000000000000000000000
χ572222-2-2-2-2-2-2-2-222-12222-2-2-1-1-111111111-1-1-1-1-1-111200-220000-200-1-1−i3i3i3−i311-1-1i3−i3−i3i3i3−i3−i3i311i3−i3−i3i300000000000000000000
χ582222-2-2-2-2-2-2-2-222-12222-2-2-1-1-111111111-1-1-1-1-1-111200-220000-200-1-1i3−i3−i3i311-1-1−i3i3i3−i3−i3i3i3−i311−i3i3i3−i300000000000000000000
χ592222-2-2-2-2-2-2-2-222-12222-2-2-1-1-111111111-1-1-1-1-1-111-2002-2000020011−i3i3−i3i3-1-111i3−i3−i3i3−i3i3i3−i3-1-1i3−i3i3−i300000000000000000000
χ602222-2-2-2-2-2-2-2-222-12222-2-2-1-1-111111111-1-1-1-1-1-111-2002-2000020011i3−i3i3−i3-1-111−i3i3i3−i3i3−i3−i3i3-1-1−i3i3−i3i300000000000000000000
χ6122-2-22i2i−2i−2i2-22-22-222i−2i2i−2i2i−2i2-2-22i2i−2i−2i2-22-22-22i−2i2i−2i2i−2i00000000000000000000000000000000000000000000000000002i−2i2-2
χ6222-2-22i2i−2i−2i2-22-22-222i−2i2i−2i2i−2i2-2-22i2i−2i−2i2-22-22-22i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000−2i2i-22
χ6322-2-22i2i−2i−2i2-2-22-2222i−2i−2i2i−2i2i2-2-22i2i−2i−2i2-2-22-222i−2i−2i2i−2i2i00000000000000000000000000000000000022-2-22i2i−2i−2i000000000000
χ6422-2-22i2i−2i−2i2-2-22-2222i−2i−2i2i−2i2i2-2-22i2i−2i−2i2-2-22-222i−2i−2i2i−2i2i000000000000000000000000000000000000-2-222−2i−2i2i2i000000000000
χ6522-2-22i2i−2i−2i-222-2-222−2i2i2i−2i−2i2i2-2-22i2i−2i−2i-222-2-22−2i2i2i−2i−2i2i000000000000000000000000000000000000000000002-22i−2i00000000
χ6622-2-22i2i−2i−2i-222-2-222−2i2i2i−2i−2i2i2-2-22i2i−2i−2i-222-2-22−2i2i2i−2i−2i2i00000000000000000000000000000000000000000000-22−2i2i00000000
χ6722-2-22i2i−2i−2i-22-222-22−2i2i−2i2i2i−2i2-2-22i2i−2i−2i-22-222-2−2i2i−2i2i2i−2i0000000000000000000000000000000000000000000000002-22i−2i0000
χ6822-2-22i2i−2i−2i-22-222-22−2i2i−2i2i2i−2i2-2-22i2i−2i−2i-22-222-2−2i2i−2i2i2i−2i000000000000000000000000000000000000000000000000-22−2i2i0000
χ6922-2-2−2i−2i2i2i2-22-22-22−2i2i−2i2i−2i2i2-2-2−2i−2i2i2i2-22-22-2−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000000000002i−2i-22
χ7022-2-2−2i−2i2i2i2-22-22-22−2i2i−2i2i−2i2i2-2-2−2i−2i2i2i2-22-22-2−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000−2i2i2-2
χ7122-2-2−2i−2i2i2i2-2-22-222−2i2i2i−2i2i−2i2-2-2−2i−2i2i2i2-2-22-22−2i2i2i−2i2i−2i00000000000000000000000000000000000022-2-2−2i−2i2i2i000000000000
χ7222-2-2−2i−2i2i2i2-2-22-222−2i2i2i−2i2i−2i2-2-2−2i−2i2i2i2-2-22-22−2i2i2i−2i2i−2i000000000000000000000000000000000000-2-2222i2i−2i−2i000000000000
χ7322-2-2−2i−2i2i2i-222-2-2222i−2i−2i2i2i−2i2-2-2−2i−2i2i2i-222-2-222i−2i−2i2i2i−2i000000000000000000000000000000000000000000002-2−2i2i00000000
χ7422-2-2−2i−2i2i2i-222-2-2222i−2i−2i2i2i−2i2-2-2−2i−2i2i2i-222-2-222i−2i−2i2i2i−2i00000000000000000000000000000000000000000000-222i−2i00000000
χ7522-2-2−2i−2i2i2i-22-222-222i−2i2i−2i−2i2i2-2-2−2i−2i2i2i-22-222-22i−2i2i−2i−2i2i0000000000000000000000000000000000000000000000002-2−2i2i0000
χ7622-2-2−2i−2i2i2i-22-222-222i−2i2i−2i−2i2i2-2-2−2i−2i2i2i-22-222-22i−2i2i−2i−2i2i000000000000000000000000000000000000000000000000-222i−2i0000
χ7744-4-44i4i−4i−4i4-44-44-4-24i−4i4i−4i4i−4i-222−2i−2i2i2i-22-22-22−2i2i−2i2i−2i2i00000000000000000000000000000000000000000000000000000000
χ7844-4-44i4i−4i−4i4-4-44-44-24i−4i−4i4i−4i4i-222−2i−2i2i2i-222-22-2−2i2i2i−2i2i−2i00000000000000000000000000000000000000000000000000000000
χ7944-4-44i4i−4i−4i-444-4-44-2−4i4i4i−4i−4i4i-222−2i−2i2i2i2-2-222-22i−2i−2i2i2i−2i00000000000000000000000000000000000000000000000000000000
χ8044-4-44i4i−4i−4i-44-444-4-2−4i4i−4i4i4i−4i-222−2i−2i2i2i2-22-2-222i−2i2i−2i−2i2i00000000000000000000000000000000000000000000000000000000
χ8144-4-4−4i−4i4i4i4-44-44-4-2−4i4i−4i4i−4i4i-2222i2i−2i−2i-22-22-222i−2i2i−2i2i−2i00000000000000000000000000000000000000000000000000000000
χ8244-4-4−4i−4i4i4i4-4-44-44-2−4i4i4i−4i4i−4i-2222i2i−2i−2i-222-22-22i−2i−2i2i−2i2i00000000000000000000000000000000000000000000000000000000
χ8344-4-4−4i−4i4i4i-444-4-44-24i−4i−4i4i4i−4i-2222i2i−2i−2i2-2-222-2−2i2i2i−2i−2i2i00000000000000000000000000000000000000000000000000000000
χ8444-4-4−4i−4i4i4i-44-444-4-24i−4i4i−4i−4i4i-2222i2i−2i−2i2-22-2-22−2i2i−2i2i2i−2i00000000000000000000000000000000000000000000000000000000
χ854-44-44i−4i4i−4i0000004000000-44-44i−4i4i−4i0000000000000000000000000000000000000000000000002-22-22i−2i2i−2i000000000000
χ864-44-44i−4i4i−4i0000004000000-44-44i−4i4i−4i000000000000000000000000000000000000000000000000-22-22−2i2i−2i2i000000000000
χ874-44-4−4i4i−4i4i0000004000000-44-4−4i4i−4i4i0000000000000000000000000000000000000000000000002-22-2−2i2i−2i2i000000000000
χ884-44-4−4i4i−4i4i0000004000000-44-4−4i4i−4i4i000000000000000000000000000000000000000000000000-22-222i−2i2i−2i000000000000
χ894-4-444-4-440000004000000-4-444-4-440000000000000000000000000000000000000000000000002-2-222-2-22000000000000
χ904-4-444-4-440000004000000-4-444-4-44000000000000000000000000000000000000000000000000-222-2-222-2000000000000
χ914-4-44-444-40000004000000-4-44-444-40000000000000000000000000000000000000000000000002-2-22-222-2000000000000
χ924-4-44-444-40000004000000-4-44-444-4000000000000000000000000000000000000000000000000-222-22-2-22000000000000
χ938-88-88i−8i8i−8i000000-40000004-44−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ948-88-8−8i8i−8i8i000000-40000004-444i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ958-8-888-8-88000000-400000044-4-444-400000000000000000000000000000000000000000000000000000000000000000000
χ968-8-88-888-8000000-400000044-44-4-4400000000000000000000000000000000000000000000000000000000000000000000

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