Finite Group Databasebeta

← Group #10823421

Character table — Group #10823421

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order122222223444444444444666666612121212121212121212121244444444888812121212121212121212121212121212242424242424242422444444224444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ51111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ9111111111-1-1-1-1-1-1-1-111111111111-1-1-1-111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1
χ10111111111-1-1-1-1-1-1-1-111111111111-1-1-1-111-1-1-1-11111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-11111-1-1-1-111
χ11111111111-1-1-1-1-1-1-1-111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-111
χ12111111111-1-1-1-1-1-1-1-111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1-1-1111111-1-1
χ13111111111-1-1-1-1-1-1-1-111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-111
χ14111111111-1-1-1-1-1-1-1-111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-111-1-1
χ15111111111-1-1-1-1-1-1-1-111111111111-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-11111-1-111-1-1
χ16111111111-1-1-1-1-1-1-1-111111111111-1-1-1-111-1-1-1-111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1-1-111-1-111
χ172222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000002222-2-2-2-2000000000000
χ182222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2000000000000000000000000000000000000-2-2-2-22222000000000000
χ19222222222-2-2-2-22222-2-2-2-22222222-2-2-2-2-2-22222-2-200000000000000000000000000000000000022-2-2-2-222000000000000
χ20222222222-2-2-2-22222-2-2-2-22222222-2-2-2-2-2-22222-2-2000000000000000000000000000000000000-2-22222-2-2000000000000
χ2122222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ2222222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000000000
χ2322222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000000000000000
χ2422222222-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000000000000000
χ2522222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-11111-1-11111-1-122-2-222-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000000000000000
χ2622222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-11111-1-11111-1-122-2-2-2-222-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-100000000000000000000
χ2722222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-11111-1-11111-1-1-2-22222-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000
χ2822222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-11111-1-11111-1-1-2-222-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000
χ2922-22-2-22-222i2i−2i−2i2i2i−2i−2i2-22-22-2-22-22-22i2i−2i−2i2-22i2i−2i−2i2-2000000000000000000000000000000000000000000002-2002i−2i000000
χ3022-22-2-22-222i2i−2i−2i2i2i−2i−2i2-22-22-2-22-22-22i2i−2i−2i2-22i2i−2i−2i2-200000000000000000000000000000000000000000000-2200−2i2i000000
χ3122-22-2-22-222i2i−2i−2i−2i−2i2i2i-22-222-2-22-22-22i2i−2i−2i-22−2i−2i2i2i-222-22i−2i0000000022-2-22i2i−2i−2i000000000000000000000000000000000000
χ3222-22-2-22-222i2i−2i−2i−2i−2i2i2i-22-222-2-22-22-22i2i−2i−2i-22−2i−2i2i2i-22-22−2i2i00000000-2-222−2i−2i2i2i000000000000000000000000000000000000
χ3322-22-2-22-22−2i−2i2i2i2i2i−2i−2i-22-222-2-22-22-2−2i−2i2i2i-222i2i−2i−2i-222-2−2i2i0000000022-2-2−2i−2i2i2i000000000000000000000000000000000000
χ3422-22-2-22-22−2i−2i2i2i2i2i−2i−2i-22-222-2-22-22-2−2i−2i2i2i-222i2i−2i−2i-22-222i−2i00000000-2-2222i2i−2i−2i000000000000000000000000000000000000
χ3522-22-2-22-22−2i−2i2i2i−2i−2i2i2i2-22-22-2-22-22-2−2i−2i2i2i2-2−2i−2i2i2i2-2000000000000000000000000000000000000000000002-200−2i2i000000
χ3622-22-2-22-22−2i−2i2i2i−2i−2i2i2i2-22-22-2-22-22-2−2i−2i2i2i2-2−2i−2i2i2i2-200000000000000000000000000000000000000000000-22002i−2i000000
χ3722-22-2-22-2-12i2i−2i−2i−2i−2i2i2i-22-22-111-11-11−i−iii1-1ii−i−i1-12-22i−2i00000000-1-111−i−iii−i3−i3i3i333−3−3−i3−i3i3i333−3−300000000000000000000
χ3822-22-2-22-2-12i2i−2i−2i−2i−2i2i2i-22-22-111-11-11−i−iii1-1ii−i−i1-12-22i−2i00000000-1-111−i−iiii3i3−i3−i3−3−333i3i3−i3−i3−3−33300000000000000000000
χ3922-22-2-22-2-12i2i−2i−2i−2i−2i2i2i-22-22-111-11-11−i−iii1-1ii−i−i1-1-22−2i2i0000000011-1-1ii−i−i−i3−i3i3i333−3−3i3i3−i3−i3−3−33300000000000000000000
χ4022-22-2-22-2-12i2i−2i−2i−2i−2i2i2i-22-22-111-11-11−i−iii1-1ii−i−i1-1-22−2i2i0000000011-1-1ii−i−ii3i3−i3−i3−3−333−i3−i3i3i333−3−300000000000000000000
χ4122-22-2-22-2-1−2i−2i2i2i2i2i−2i−2i-22-22-111-11-11ii−i−i1-1−i−iii1-12-2−2i2i00000000-1-111ii−i−i−i3−i3i3i3−3−333−i3−i3i3i3−3−33300000000000000000000
χ4222-22-2-22-2-1−2i−2i2i2i2i2i−2i−2i-22-22-111-11-11ii−i−i1-1−i−iii1-12-2−2i2i00000000-1-111ii−i−ii3i3−i3−i333−3−3i3i3−i3−i333−3−300000000000000000000
χ4322-22-2-22-2-1−2i−2i2i2i2i2i−2i−2i-22-22-111-11-11ii−i−i1-1−i−iii1-1-222i−2i0000000011-1-1−i−iii−i3−i3i3i3−3−333i3i3−i3−i333−3−300000000000000000000
χ4422-22-2-22-2-1−2i−2i2i2i2i2i−2i−2i-22-22-111-11-11ii−i−i1-1−i−iii1-1-222i−2i0000000011-1-1−i−iiii3i3−i3−i333−3−3−i3−i3i3i3−3−33300000000000000000000
χ452-22-22-22-222i−2i2i−2i2i−2i2i−2i2-2-22-22-2-222-22i−2i2i−2i-222i−2i2i−2i2-2000000002i−2i2-200000000000000002i−2i2i−2i2-22-200000000000000000000
χ462-22-22-22-222i−2i2i−2i2i−2i2i−2i2-2-22-22-2-222-22i−2i2i−2i-222i−2i2i−2i2-200000000−2i2i-220000000000000000−2i2i−2i2i-22-2200000000000000000000
χ472-22-22-22-222i−2i2i−2i−2i2i−2i2i-222-2-22-2-222-22i−2i2i−2i2-2−2i2i−2i2i-2200000000000000000000000000000000000000000000000000002-22i−2i
χ482-22-22-22-222i−2i2i−2i−2i2i−2i2i-222-2-22-2-222-22i−2i2i−2i2-2−2i2i−2i2i-220000000000000000000000000000000000000000000000000000-22−2i2i
χ492-22-22-22-22−2i2i−2i2i2i−2i2i−2i-222-2-22-2-222-2−2i2i−2i2i2-22i−2i2i−2i-2200000000000000000000000000000000000000000000000000002-2−2i2i
χ502-22-22-22-22−2i2i−2i2i2i−2i2i−2i-222-2-22-2-222-2−2i2i−2i2i2-22i−2i2i−2i-220000000000000000000000000000000000000000000000000000-222i−2i
χ512-22-22-22-22−2i2i−2i2i−2i2i−2i2i2-2-22-22-2-222-2−2i2i−2i2i-22−2i2i−2i2i2-2000000002i−2i-2200000000000000002i−2i2i−2i-22-2200000000000000000000
χ522-22-22-22-22−2i2i−2i2i−2i2i−2i2i2-2-22-22-2-222-2−2i2i−2i2i-22−2i2i−2i2i2-200000000−2i2i2-20000000000000000−2i2i−2i2i2-22-200000000000000000000
χ532-22-22-22-2-12i−2i2i−2i2i−2i2i−2i2-2-221-111-1-11−ii−ii1-1−ii−ii-11000000002i−2i2-23−33−3−i3i3−i3i3−i3i3−i3i33−33−3−ii−ii-11-1100000000000000000000
χ542-22-22-22-2-12i−2i2i−2i2i−2i2i−2i2-2-221-111-1-11−ii−ii1-1−ii−ii-11000000002i−2i2-2−33−33i3−i3i3−i3i3−i3i3−i3−33−33−ii−ii-11-1100000000000000000000
χ552-22-22-22-2-12i−2i2i−2i2i−2i2i−2i2-2-221-111-1-11−ii−ii1-1−ii−ii-1100000000−2i2i-223−33−3−i3i3−i3i3i3−i3i3−i3−33−33i−ii−i1-11-100000000000000000000
χ562-22-22-22-2-12i−2i2i−2i2i−2i2i−2i2-2-221-111-1-11−ii−ii1-1−ii−ii-1100000000−2i2i-22−33−33i3−i3i3−i3−i3i3−i3i33−33−3i−ii−i1-11-100000000000000000000
χ572-22-22-22-2-1−2i2i−2i2i−2i2i−2i2i2-2-221-111-1-11i−ii−i1-1i−ii−i-11000000002i−2i-223−33−3i3−i3i3−i3−i3i3−i3i3−33−33−ii−ii1-11-100000000000000000000
χ582-22-22-22-2-1−2i2i−2i2i−2i2i−2i2i2-2-221-111-1-11i−ii−i1-1i−ii−i-11000000002i−2i-22−33−33−i3i3−i3i3i3−i3i3−i33−33−3−ii−ii1-11-100000000000000000000
χ592-22-22-22-2-1−2i2i−2i2i−2i2i−2i2i2-2-221-111-1-11i−ii−i1-1i−ii−i-1100000000−2i2i2-23−33−3i3−i3i3−i3i3−i3i3−i33−33−3i−ii−i-11-1100000000000000000000
χ602-22-22-22-2-1−2i2i−2i2i−2i2i−2i2i2-2-221-111-1-11i−ii−i1-1i−ii−i-1100000000−2i2i2-2−33−33−i3i3−i3i3−i3i3−i3i3−33−33i−ii−i-11-1100000000000000000000
χ612-2-2-2-222222-2-222-2-2222-2-2-2-22-2-2222-2-22-2-22-2-222200000000000000000000000000000000000000000000002-2002-20000
χ622-2-2-2-222222-2-222-2-2222-2-2-2-22-2-2222-2-22-2-22-2-22220000000000000000000000000000000000000000000000-2200-220000
χ632-2-2-2-222222-2-22-222-2-2-222-2-22-2-2222-2-2222-222-2-2-200002-22-20000000000002-2-222-2-220000000000000000000000000000
χ642-2-2-2-222222-2-22-222-2-2-222-2-22-2-2222-2-2222-222-2-2-20000-22-22000000000000-222-2-222-20000000000000000000000000000
χ652-2-2-2-22222-222-22-2-22-2-222-2-22-2-222-222-2222-2-22-2-200002-2-220000000000002-2-22-222-20000000000000000000000000000
χ662-2-2-2-22222-222-22-2-22-2-222-2-22-2-222-222-2222-2-22-2-20000-222-2000000000000-222-22-2-220000000000000000000000000000
χ672-2-2-2-22222-222-2-222-222-2-2-2-22-2-222-222-2-2-2-222-22200000000000000000000000000000000000000000000002-200-220000
χ682-2-2-2-22222-222-2-222-222-2-2-2-22-2-222-222-2-2-2-222-2220000000000000000000000000000000000000000000000-22002-20000
χ692-2-2-2-2222-12-2-22-222-2-2-22211-111-1-1-111-1-1-11-1-111100002-22-200003−3−33−333−3-111-1-111-13−3−33−333−300000000000000000000
χ702-2-2-2-2222-12-2-22-222-2-2-22211-111-1-1-111-1-1-11-1-111100002-22-20000−333−33−3−33-111-1-111-1−333−33−3−3300000000000000000000
χ712-2-2-2-2222-12-2-22-222-2-2-22211-111-1-1-111-1-1-11-1-11110000-22-2200003−3−33−333−31-1-111-1-11−333−33−3−3300000000000000000000
χ722-2-2-2-2222-12-2-22-222-2-2-22211-111-1-1-111-1-1-11-1-11110000-22-220000−333−33−3−331-1-111-1-113−3−33−333−300000000000000000000
χ732-2-2-2-2222-1-222-22-2-22-2-22211-111-1-11-1-11-1-1-111-11100002-2-2200003−3−333−3−33-111-11-1-113−3−333−3−3300000000000000000000
χ742-2-2-2-2222-1-222-22-2-22-2-22211-111-1-11-1-11-1-1-111-11100002-2-220000−333−3−333−3-111-11-1-11−333−3−333−300000000000000000000
χ752-2-2-2-2222-1-222-22-2-22-2-22211-111-1-11-1-11-1-1-111-1110000-222-200003−3−333−3−331-1-11-111-1−333−3−333−300000000000000000000
χ762-2-2-2-2222-1-222-22-2-22-2-22211-111-1-11-1-11-1-1-111-1110000-222-20000−333−3−333−31-1-11-111-13−3−333−3−3300000000000000000000
χ7744444444-24444-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000000000000000
χ7844444444-2-4-4-4-44444-4-4-4-4-2-2-2-2-2-2-2222222-2-2-2-22200000000000000000000000000000000000000000000000000000000
χ79444-4-4-4-44400000000000044-4-4-4-4400000000000000000000000000000000000000000000000000004i−4i00000000000000
χ80444-4-4-4-44400000000000044-4-4-4-440000000000000000000000000000000000000000000000000000−4i4i00000000000000
χ8144-44-4-44-4-24i4i−4i−4i4i4i−4i−4i4-44-4-222-22-22−2i−2i2i2i-22−2i−2i2i2i-2200000000000000000000000000000000000000000000000000000000
χ8244-44-4-44-4-2−4i−4i4i4i−4i−4i4i4i4-44-4-222-22-222i2i−2i−2i-222i2i−2i−2i-2200000000000000000000000000000000000000000000000000000000
χ8344-4-444-4-440000000000004-44-44-4-4000000000000000000000000000000000000000000000000004-40000000000000000
χ8444-4-444-4-440000000000004-44-44-4-400000000000000000000000000000000000000000000000000-440000000000000000
χ854-444-44-4-44000000000000-4444-4-4-40000000000000000000000000000000000000000000000004-4000000000000000000
χ864-444-44-4-44000000000000-4444-4-4-4000000000000000000000000000000000000000000000000-44000000000000000000
χ874-44-44-44-4-24i−4i4i−4i−4i4i−4i4i-444-42-222-2-22−2i2i−2i2i-222i−2i2i−2i2-200000000000000000000000000000000000000000000000000000000
χ884-44-44-44-4-2−4i4i−4i4i4i−4i4i−4i-444-42-222-2-222i−2i2i−2i-22−2i2i−2i2i2-200000000000000000000000000000000000000000000000000000000
χ894-4-444-4-444000000000000-4-4-444-440000000000000000000000000000000000000000000000000000004-4000000000000
χ904-4-444-4-444000000000000-4-4-444-44000000000000000000000000000000000000000000000000000000-44000000000000
χ914-4-4-4-4444-24-4-444-4-4444-4-422-222-2-2-222-222-222-2-2-200000000000000000000000000000000000000000000000000000000
χ924-4-4-4-4444-2-444-4-444-444-4-422-222-2-22-2-22222-2-22-2-200000000000000000000000000000000000000000000000000000000
χ93888-8-8-8-88-4000000000000-4-44444-400000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-888-8-8-4000000000000-44-44-44400000000000000000000000000000000000000000000000000000000000000000000
χ958-888-88-8-8-40000000000004-4-4-444400000000000000000000000000000000000000000000000000000000000000000000
χ968-8-888-8-88-4000000000000444-4-44-400000000000000000000000000000000000000000000000000000000000000000000

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