Finite Group Databasebeta

← Group #10822700

Character table — Group #10822700

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order12222222222234444444466666666666121212121212121244444444888812121212121212121212121212121212242424242424242422224444224444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ51111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
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
χ911111111-1-1-1-1111-1-1-1-1111111111-1-1-1-1111-1-1-1-1111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-111-1-1
χ1011111111-1-1-1-1111-1-1-1-1111111111-1-1-1-1111-1-1-1-1111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-111
χ1111111111-1-1-1-1111-1-1-1-1111111111-1-1-1-1111-1-1-1-1111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-111-1-1-1-111
χ1211111111-1-1-1-1111-1-1-1-1111111111-1-1-1-1111-1-1-1-1111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111-1-11111-1-1
χ1311111111-1-1-1-1111-1-1-1-1111111111-1-1-1-1111-1-1-1-11-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-111-1-111
χ1411111111-1-1-1-1111-1-1-1-1111111111-1-1-1-1111-1-1-1-11-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-111-1-111-1-1
χ1511111111-1-1-1-1111-1-1-1-1111111111-1-1-1-1111-1-1-1-11-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1111111-1-1
χ1611111111-1-1-1-1111-1-1-1-1111111111-1-1-1-1111-1-1-1-11-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111
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
χ19222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ20222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000000000
χ21222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000000000000000
χ22222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000000000000000
χ2322222222-2-2-2-22-2-22222-2-22222222-2-2-2-2-2-2-22222-200000000000000000000000000000000000022-2-2-2-222000000000000
χ2422222222-2-2-2-22-2-22222-2-22222222-2-2-2-2-2-2-22222-2000000000000000000000000000000000000-2-22222-2-2000000000000
χ2522222222-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-11111-1-1-11111-122-2-222-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000000000000000
χ2622222222-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-11111-1-1-11111-122-2-2-2-222-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-100000000000000000000
χ2722222222-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-11111-1-1-11111-1-2-22222-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000
χ2822222222-2-2-2-2-122-2-2-2-222-1-1-1-1-1-1-11111-1-1-11111-1-2-222-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000
χ29222-2-2-2-2222-2-222-222-2-22-222-2-22-2-222-2-22-2-222-2-2200002i−2i2i−2i0000000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ30222-2-2-2-2222-2-222-222-2-22-222-2-22-2-222-2-22-2-222-2-220000−2i2i−2i2i000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ31222-2-2-2-2222-2-22-22-2-222-2222-2-22-2-222-2-2-222-2-222-200000000000000000000000000000000000000000000002i−2i2i−2i000000
χ32222-2-2-2-2222-2-22-22-2-222-2222-2-22-2-222-2-2-222-2-222-20000000000000000000000000000000000000000000000−2i2i−2i2i000000
χ33222-2-2-2-2222-2-2-12-222-2-22-2-1-111-111-1-111-111-1-111-100002i−2i2i−2i000033−3−333−3−3−i−iii−i−iii−i3−i3i3i3−i3−i3i3i300000000000000000000
χ34222-2-2-2-2222-2-2-12-222-2-22-2-1-111-111-1-111-111-1-111-100002i−2i2i−2i0000−3−333−3−333−i−iii−i−iiii3i3−i3−i3i3i3−i3−i300000000000000000000
χ35222-2-2-2-2222-2-2-12-222-2-22-2-1-111-111-1-111-111-1-111-10000−2i2i−2i2i000033−3−333−3−3ii−i−iii−i−ii3i3−i3−i3i3i3−i3−i300000000000000000000
χ36222-2-2-2-2222-2-2-12-222-2-22-2-1-111-111-1-111-111-1-111-10000−2i2i−2i2i0000−3−333−3−333ii−i−iii−i−i−i3−i3i3i3−i3−i3i3i300000000000000000000
χ37222-2-2-2-22-2-22222-2-2-2222-222-2-22-2-2-2-2222-2-2-2-222200002i−2i−2i2i0000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ38222-2-2-2-22-2-22222-2-2-2222-222-2-22-2-2-2-2222-2-2-2-22220000−2i2i2i−2i000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ39222-2-2-2-22-2-2222-2222-2-2-2222-2-22-2-2-2-222-22222-2-2-200000000000000000000000000000000000000000000002i−2i−2i2i000000
χ40222-2-2-2-22-2-2222-2222-2-2-2222-2-22-2-2-2-222-22222-2-2-20000000000000000000000000000000000000000000000−2i2i2i−2i000000
χ41222-2-2-2-22-2-222-12-2-2-2222-2-1-111-11111-1-1-11111-1-1-100002i−2i−2i2i000033−3−3−3−333−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i300000000000000000000
χ42222-2-2-2-22-2-222-12-2-2-2222-2-1-111-11111-1-1-11111-1-1-100002i−2i−2i2i0000−3−33333−3−3−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i300000000000000000000
χ43222-2-2-2-22-2-222-12-2-2-2222-2-1-111-11111-1-1-11111-1-1-10000−2i2i2i−2i000033−3−3−3−333ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i300000000000000000000
χ44222-2-2-2-22-2-222-12-2-2-2222-2-1-111-11111-1-1-11111-1-1-10000−2i2i2i−2i0000−3−33333−3−3ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i300000000000000000000
χ452-2-22-2-2222-22-22222-22-2-2-2-2-2222-2-22-22-222-22-22-2-200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ462-2-22-2-2222-22-22222-22-2-2-2-2-2222-2-22-22-222-22-22-2-20000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ472-2-22-2-2222-22-22-2-2-22-2222-2-2222-2-22-22-2-2-22-22-222000000002-22-200000000000000002-22-22-22-200000000000000000000
χ482-2-22-2-2222-22-22-2-2-22-2222-2-2222-2-22-22-2-2-22-22-22200000000-22-220000000000000000-22-22-22-2200000000000000000000
χ492-2-22-2-2222-22-2-1-2-2-22-222211-1-1-111-11-1111-11-11-1-1000000002-22-23−33−33−33−33−33−33−33−3-11-11-11-1100000000000000000000
χ502-2-22-2-2222-22-2-1-2-2-22-222211-1-1-111-11-1111-11-11-1-1000000002-22-2−33−33−33−33−33−33−33−33-11-11-11-1100000000000000000000
χ512-2-22-2-2222-22-2-1-2-2-22-222211-1-1-111-11-1111-11-11-1-100000000-22-223−33−33−33−3−33−33−33−331-11-11-11-100000000000000000000
χ522-2-22-2-2222-22-2-1-2-2-22-222211-1-1-111-11-1111-11-11-1-100000000-22-22−33−33−33−333−33−33−33−31-11-11-11-100000000000000000000
χ532-2-22-2-222-22-22222-22-22-2-2-2-2222-2-2-22-2222-2-22-22-200000000000000000000000000000000000000000000000000002i−2i−2i2i
χ542-2-22-2-222-22-22222-22-22-2-2-2-2222-2-2-22-2222-2-22-22-20000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ552-2-22-2-222-22-222-2-22-22-222-2-2222-2-2-22-22-2-222-22-22000000002-2-2200000000000000002-22-2-22-2200000000000000000000
χ562-2-22-2-222-22-222-2-22-22-222-2-2222-2-2-22-22-2-222-22-2200000000-222-20000000000000000-22-222-22-200000000000000000000
χ572-2-22-2-222-22-22-1-2-22-22-22211-1-1-1111-11-111-1-11-11-1000000002-2-223−33−3−33−333−33−3−33−33-11-111-11-100000000000000000000
χ582-2-22-2-222-22-22-1-2-22-22-22211-1-1-1111-11-111-1-11-11-1000000002-2-22−33−333−33−3−33−333−33−3-11-111-11-100000000000000000000
χ592-2-22-2-222-22-22-1-2-22-22-22211-1-1-1111-11-111-1-11-11-100000000-222-23−33−3−33−33−33−333−33−31-11-1-11-1100000000000000000000
χ602-2-22-2-222-22-22-1-2-22-22-22211-1-1-1111-11-111-1-11-11-100000000-222-2−33−333−33−33−33−3−33−331-11-1-11-1100000000000000000000
χ612-2-2-222-222-2-2222-22-2-22-22-2-2-2-22222-2-222-222-2-22-2000000000000000000000000000000000000000000002-200002-20000
χ622-2-2-222-222-2-2222-22-2-22-22-2-2-2-22222-2-222-222-2-22-200000000000000000000000000000000000000000000-220000-220000
χ632-2-2-222-222-2-222-22-222-22-2-2-2-2-22222-2-22-22-2-222-222-22-2000000002-2-222-2-22000000000000000000000000000000000000
χ642-2-2-222-222-2-222-22-222-22-2-2-2-2-22222-2-22-22-2-222-22-22-2200000000-222-2-222-2000000000000000000000000000000000000
χ652-2-2-222-222-2-22-1-22-222-22-21111-1-1-1-111-11-111-1-11-12-22-200000000-111-1-111-1−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i300000000000000000000
χ662-2-2-222-222-2-22-1-22-222-22-21111-1-1-1-111-11-111-1-11-12-22-200000000-111-1-111-1i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i300000000000000000000
χ672-2-2-222-222-2-22-1-22-222-22-21111-1-1-1-111-11-111-1-11-1-22-22000000001-1-111-1-11−i3i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3−i3i300000000000000000000
χ682-2-2-222-222-2-22-1-22-222-22-21111-1-1-1-111-11-111-1-11-1-22-22000000001-1-111-1-11i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3i3−i300000000000000000000
χ692-2-2-222-22-222-222-2-222-2-22-2-2-2-2222-222-22-22-222-2-2000000000000000000000000000000000000000000002-20000-220000
χ702-2-2-222-22-222-222-2-222-2-22-2-2-2-2222-222-22-22-222-2-200000000000000000000000000000000000000000000-2200002-20000
χ712-2-2-222-22-222-22-222-2-222-2-2-2-2-2222-222-2-22-22-2-2222-2-22000000002-2-22-222-2000000000000000000000000000000000000
χ722-2-2-222-22-222-22-222-2-222-2-2-2-2-2222-222-2-22-22-2-222-222-200000000-222-22-2-22000000000000000000000000000000000000
χ732-2-2-222-22-222-2-1-222-2-222-21111-1-1-11-1-111-11-111-1-12-2-2200000000-111-11-1-11−i3i3i3−i3i3−i3−i3i3−i3i3i3−i3i3−i3−i3i300000000000000000000
χ742-2-2-222-22-222-2-1-222-2-222-21111-1-1-11-1-111-11-111-1-12-2-2200000000-111-11-1-11i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i300000000000000000000
χ752-2-2-222-22-222-2-1-222-2-222-21111-1-1-11-1-111-11-111-1-1-222-2000000001-1-11-111-1−i3i3i3−i3i3−i3−i3i3i3−i3−i3i3−i3i3i3−i300000000000000000000
χ762-2-2-222-22-222-2-1-222-2-222-21111-1-1-11-1-111-11-111-1-1-222-2000000001-1-11-111-1i3−i3−i3i3−i3i3i3−i3−i3i3i3−i3i3−i3−i3i300000000000000000000
χ77444444444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000000000000000
χ7844444444-4-4-4-4-2-4-44444-4-4-2-2-2-2-2-2-22222222-2-2-2-2200000000000000000000000000000000000000000000000000000000
χ79444-4-4-4-4444-4-4-2-44-4-444-44-2-222-222-2-2222-2-222-2-2200000000000000000000000000000000000000000000000000000000
χ80444-4-4-4-44-4-444-2-4444-4-4-44-2-222-22222-2-22-2-2-2-222200000000000000000000000000000000000000000000000000000000
χ8144-444-4-4-400004000000004-44-4-44-40000000000000000000000000000000000000000000000004-4000000000000000000
χ8244-444-4-4-400004000000004-44-4-44-4000000000000000000000000000000000000000000000000-44000000000000000000
χ8344-4-4-444-400004000000004-4-44-4-44000000000000000000000000000000000000000000000000004-40000000000000000
χ8444-4-4-444-400004000000004-4-44-4-4400000000000000000000000000000000000000000000000000-440000000000000000
χ854-444-44-4-40000400000000-444-4-4-4400000000000000000000000000000000000000000000000000004i−4i00000000000000
χ864-444-44-4-40000400000000-444-4-4-440000000000000000000000000000000000000000000000000000−4i4i00000000000000
χ874-44-44-44-40000400000000-44-44-44-40000000000000000000000000000000000000000000000000000004i−4i000000000000
χ884-44-44-44-40000400000000-44-44-44-4000000000000000000000000000000000000000000000000000000−4i4i000000000000
χ894-4-44-4-4444-44-4-2444-44-4-4-422-2-2-222-22-22-2-22-22-22200000000000000000000000000000000000000000000000000000000
χ904-4-44-4-444-44-44-244-44-44-4-422-2-2-2222-22-2-2-222-22-2200000000000000000000000000000000000000000000000000000000
χ914-4-4-444-444-4-44-24-44-4-44-442222-2-2-2-222-2-22-2-222-2200000000000000000000000000000000000000000000000000000000
χ924-4-4-444-44-444-4-24-4-444-4-442222-2-2-22-2-22-22-22-2-22200000000000000000000000000000000000000000000000000000000
χ9388-888-8-8-80000-400000000-44-444-4400000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8-888-80000-400000000-444-444-400000000000000000000000000000000000000000000000000000000000000000000
χ958-888-88-8-80000-4000000004-4-4444-400000000000000000000000000000000000000000000000000000000000000000000
χ968-88-88-88-80000-4000000004-44-44-4400000000000000000000000000000000000000000000000000000000000000000000

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