Finite Group Databasebeta

← Group #10823174

Character table — Group #10823174

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order122222222222344444444666666666661212121212121212222244444444666666661212121212121212121212121212121288888888224444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
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
χ911111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ1111111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ1211111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1
χ1311111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111
χ1411111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ1511111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1
χ1611111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ172222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2000000002-22-2000000000000000022-2-222-2-200000000000000000000
χ182222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-200000000-22-220000000000000000-2-222-2-22200000000000000000000
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
χ23222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111000000002-22-2−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3-1-111-1-11100000000000000000000
χ24222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111000000002-22-2i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3-1-111-1-11100000000000000000000
χ25222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111100000000-22-22−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i311-1-111-1-100000000000000000000
χ26222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111100000000-22-22i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i311-1-111-1-100000000000000000000
χ2722222222-2-2-2-22-2-2-22222-22222222-2-2-2-2-2-2-2-22222000000002-2-22000000000000000022-2-2-2-22200000000000000000000
χ2822222222-2-2-2-22-2-2-22222-22222222-2-2-2-2-2-2-2-2222200000000-222-20000000000000000-2-22222-2-200000000000000000000
χ2922222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-11111-1-1-1-1111122-2-222-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000000000000000
χ3022222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-11111-1-1-1-1111122-2-2-2-222-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-100000000000000000000
χ3122222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-11111-1-1-1-11111-2-22222-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000
χ3222222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-11111-1-1-1-11111-2-222-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000
χ3322222222-2-2-2-2-1-2-2-22222-2-1-1-1-1-1-1-111111111-1-1-1-1000000002-2-22−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-1-11111-1-100000000000000000000
χ3422222222-2-2-2-2-1-2-2-22222-2-1-1-1-1-1-1-111111111-1-1-1-1000000002-2-22i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-1-11111-1-100000000000000000000
χ3522222222-2-2-2-2-1-2-2-22222-2-1-1-1-1-1-1-111111111-1-1-1-100000000-222-2−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i311-1-1-1-11100000000000000000000
χ3622222222-2-2-2-2-1-2-2-22222-2-1-1-1-1-1-1-111111111-1-1-1-100000000-222-2i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i311-1-1-1-11100000000000000000000
χ3722-2-2-2-22222-2-2222-222-2-2-2222-2-2-2-222-2-222-2-222-2-200002i−2i2i−2i0000000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ3822-2-2-2-22222-2-2222-222-2-2-2222-2-2-2-222-2-222-2-222-2-20000−2i2i−2i2i000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ3922-2-2-2-22222-2-22-2-22-2-2222222-2-2-2-222-2-2-2-222-2-2222-22-2000000002-22-22-22-2000000000000000000000000000000000000
χ4022-2-2-2-22222-2-22-2-22-2-2222222-2-2-2-222-2-2-2-222-2-222-22-2200000000-22-22-22-22000000000000000000000000000000000000
χ4122-2-2-2-22222-2-2-122-222-2-2-2-1-1-11111-1-111-1-111-1-11100002i−2i2i−2i0000−i3i3i3−i3−i3i3i3−i3−ii−ii−ii−ii3−33−33−33−300000000000000000000
χ4222-2-2-2-22222-2-2-122-222-2-2-2-1-1-11111-1-111-1-111-1-11100002i−2i2i−2i0000i3−i3−i3i3i3−i3−i3i3−ii−ii−ii−ii−33−33−33−3300000000000000000000
χ4322-2-2-2-22222-2-2-122-222-2-2-2-1-1-11111-1-111-1-111-1-1110000−2i2i−2i2i0000−i3i3i3−i3−i3i3i3−i3i−ii−ii−ii−i−33−33−33−3300000000000000000000
χ4422-2-2-2-22222-2-2-122-222-2-2-2-1-1-11111-1-111-1-111-1-1110000−2i2i−2i2i0000i3−i3−i3i3i3−i3−i3i3i−ii−ii−ii−i3−33−33−33−300000000000000000000
χ4522-2-2-2-22222-2-2-1-2-22-2-2222-1-1-11111-1-11111-1-111-1-12-22-200000000-11-11-11-113−3−333−3−333−3−333−3−3300000000000000000000
χ4622-2-2-2-22222-2-2-1-2-22-2-2222-1-1-11111-1-11111-1-111-1-12-22-200000000-11-11-11-11−333−3−333−3−333−3−333−300000000000000000000
χ4722-2-2-2-22222-2-2-1-2-22-2-2222-1-1-11111-1-11111-1-111-1-1-22-22000000001-11-11-11-13−3−333−3−33−333−3−333−300000000000000000000
χ4822-2-2-2-22222-2-2-1-2-22-2-2222-1-1-11111-1-11111-1-111-1-1-22-22000000001-11-11-11-1−333−3−333−33−3−333−3−3300000000000000000000
χ4922-2-2-2-222-2-222222-2-2-222-2222-2-2-2-2-2-22222-2-2-2-22200002i−2i−2i2i0000000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ5022-2-2-2-222-2-222222-2-2-222-2222-2-2-2-2-2-22222-2-2-2-2220000−2i2i2i−2i000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ5122-2-2-2-222-2-2222-2-2222-2-22222-2-2-2-2-2-222-2-22222-2-22-2-22000000002-22-2-22-22000000000000000000000000000000000000
χ5222-2-2-2-222-2-2222-2-2222-2-22222-2-2-2-2-2-222-2-22222-2-2-222-200000000-22-222-22-2000000000000000000000000000000000000
χ5322-2-2-2-222-2-222-122-2-2-222-2-1-1-1111111-1-1-1-11111-1-100002i−2i−2i2i0000−i3i3i3−i3i3−i3−i3i3−ii−iii−ii−i3−33−3−33−3300000000000000000000
χ5422-2-2-2-222-2-222-122-2-2-222-2-1-1-1111111-1-1-1-11111-1-100002i−2i−2i2i0000i3−i3−i3i3−i3i3i3−i3−ii−iii−ii−i−33−333−33−300000000000000000000
χ5522-2-2-2-222-2-222-122-2-2-222-2-1-1-1111111-1-1-1-11111-1-10000−2i2i2i−2i0000−i3i3i3−i3i3−i3−i3i3i−ii−i−ii−ii−33−333−33−300000000000000000000
χ5622-2-2-2-222-2-222-122-2-2-222-2-1-1-1111111-1-1-1-11111-1-10000−2i2i2i−2i0000i3−i3−i3i3−i3i3i3−i3i−ii−i−ii−ii3−33−3−33−3300000000000000000000
χ5722-2-2-2-222-2-222-1-2-2222-2-22-1-1-1111111-1-111-1-1-1-1112-2-2200000000-11-111-11-13−3−33−333−33−3−33−333−300000000000000000000
χ5822-2-2-2-222-2-222-1-2-2222-2-22-1-1-1111111-1-111-1-1-1-1112-2-2200000000-11-111-11-1−333−33−3−33−333−33−3−3300000000000000000000
χ5922-2-2-2-222-2-222-1-2-2222-2-22-1-1-1111111-1-111-1-1-1-111-222-2000000001-11-1-11-113−3−33−333−3−333−33−3−3300000000000000000000
χ6022-2-2-2-222-2-222-1-2-2222-2-22-1-1-1111111-1-111-1-1-1-111-222-2000000001-11-1-11-11−333−33−3−333−3−33−333−300000000000000000000
χ612-222-2-22-22-22-222-222-22-2-2-2-2222-2-22-22-22-22-22-22-20000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ622-222-2-22-22-22-222-222-22-2-2-2-2222-2-22-22-22-22-22-22-2000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ632-222-2-22-22-22-22-22-2-22-222-2-2222-2-22-22-2-22-22-22-22000000000000000000000000000000000000000000002-22-200000000
χ642-222-2-22-22-22-22-22-2-22-222-2-2222-2-22-22-2-22-22-22-2200000000000000000000000000000000000000000000-22-2200000000
χ652-222-2-22-2-22-2222-22-22-22-2-2-2222-2-2-22-222-22-2-22-220000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ662-222-2-22-2-22-2222-22-22-22-2-2-2222-2-2-22-222-22-2-22-22000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ672-222-2-22-2-22-222-22-22-22-22-2-2222-2-2-22-22-22-222-22-2000000000000000000000000000000000000000000002-2-2200000000
χ682-222-2-22-2-22-222-22-22-22-22-2-2222-2-2-22-22-22-222-22-200000000000000000000000000000000000000000000-222-200000000
χ692-2-2-2222-22-2-2222-2-22-2-222-2-22-2-2222-2-222-2-222-2-2200000000000000000000000000000000000000000000000000002-22-2
χ702-2-2-2222-22-2-2222-2-22-2-222-2-22-2-2222-2-222-2-222-2-220000000000000000000000000000000000000000000000000000-22-22
χ712-2-2-2222-22-2-222-222-222-2-2-2-22-2-2222-2-22-222-2-222-20000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ722-2-2-2222-22-2-222-222-222-2-2-2-22-2-2222-2-22-222-2-222-2000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ732-2-2-2222-2-222-222-2-2-222-22-2-22-2-222-222-22-2-22-222-200000000000000000000000000000000000000000000000000002-2-22
χ742-2-2-2222-2-222-222-2-2-222-22-2-22-2-222-222-22-2-22-222-20000000000000000000000000000000000000000000000000000-222-2
χ752-2-2-2222-2-222-22-2222-2-22-2-2-22-2-222-222-2-222-22-2-220000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ762-2-2-2222-2-222-22-2222-2-22-2-2-22-2-222-222-2-222-22-2-22000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ77444-44-4-4-400004000000004-4-44-44-40000000000000000000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ78444-44-4-4-400004000000004-4-44-44-400000000000000000000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ7944-44-44-4-400004000000004-4-4-44-44000000000000000000000000000000000000000000000000−2i22i2−2i22i20000000000000000
χ8044-44-44-4-400004000000004-4-4-44-440000000000000000000000000000000000000000000000002i2−2i22i2−2i20000000000000000
χ814-444-4-44-44-44-4-24-444-44-4-422-2-2-222-22-22-22-22-22-2200000000000000000000000000000000000000000000000000000000
χ824-444-4-44-44-44-4-2-44-4-44-44422-2-2-222-22-222-22-22-22-200000000000000000000000000000000000000000000000000000000
χ834-444-4-44-4-44-44-24-44-44-44-422-2-2-2222-22-2-22-222-22-200000000000000000000000000000000000000000000000000000000
χ844-444-4-44-4-44-44-2-44-44-44-4422-2-2-2222-22-22-22-2-22-2200000000000000000000000000000000000000000000000000000000
χ854-44-4-44-440000400000000-44-44-4-4400000000000000000000000000000000000000000000000022−22−22220000000000000000
χ864-44-4-44-440000400000000-44-44-4-44000000000000000000000000000000000000000000000000−222222−220000000000000000
χ874-4-444-4-440000400000000-44-4-444-4000000000000000000000000000000000000000000000000000022−22−2222000000000000
χ884-4-444-4-440000400000000-44-4-444-40000000000000000000000000000000000000000000000000000−222222−22000000000000
χ894-4-4-4444-44-4-44-24-4-44-4-44422-222-2-2-222-2-222-2-222-200000000000000000000000000000000000000000000000000000000
χ904-4-4-4444-44-4-44-2-444-444-4-422-222-2-2-222-22-2-222-2-2200000000000000000000000000000000000000000000000000000000
χ914-4-4-4444-4-444-4-24-4-4-444-4422-222-2-22-2-22-222-22-2-2200000000000000000000000000000000000000000000000000000000
χ924-4-4-4444-4-444-4-2-4444-4-44-422-222-2-22-2-222-2-22-222-200000000000000000000000000000000000000000000000000000000
χ93888-88-8-8-80000-400000000-444-44-4400000000000000000000000000000000000000000000000000000000000000000000
χ9488-88-88-8-80000-400000000-4444-44-400000000000000000000000000000000000000000000000000000000000000000000
χ958-88-8-88-880000-4000000004-44-444-400000000000000000000000000000000000000000000000000000000000000000000
χ968-8-888-8-880000-4000000004-444-4-4400000000000000000000000000000000000000000000000000000000000000000000

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