Finite Group Databasebeta

← Group #10823164

Character table — Group #10823164

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order1222222222223444444446666666666612121212121212122244444444446666121212121212121212121212121212121212121288888888224444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ911111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ1011111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ1111111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111
χ1211111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-111-1-1
χ1311111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1
χ1411111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ1511111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111
χ1611111111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ172222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2002-22-2000000000022-2-222-2-200000000000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-200-22-220000000000-2-222-2-22200000000000000000000000000000000
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
χ20222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-222-1-1-1-111111111-1-1-1-11111111100000000000000000000
χ21222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-2-2-2-2-21111-1-1-1-1-1-1-1-111111111111100000000000000000000
χ22222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-22222-2-21111111111111111-1-1-1-1-1-1-1-100000000000000000000
χ23222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111002-22-2000000−i3−i3i3i3-1-111-1-111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300000000000000000000
χ24222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111002-22-2000000i3i3−i3−i3-1-111-1-111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300000000000000000000
χ25222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111100-22-22000000−i3−i3i3i311-1-111-1-1−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300000000000000000000
χ26222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111100-22-22000000i3i3−i3−i311-1-111-1-1i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300000000000000000000
χ2722222222-2-2-2-22-2-2-22222-22222222-2-2-2-2-2-2-2-22222002-2-22000000000022-2-2-2-22200000000000000000000000000000000
χ2822222222-2-2-2-22-2-2-22222-22222222-2-2-2-2-2-2-2-2222200-222-20000000000-2-22222-2-200000000000000000000000000000000
χ2922222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-11111-1-1-1-111112222-2-222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-1111100000000000000000000
χ3022222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-11111-1-1-1-1111122-2-222-2-222-2-2-1-1-1-11111-1-1-1-111111111-1-1-1-100000000000000000000
χ3122222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-11111-1-1-1-11111-2-222-2-2-2-222221111-1-1-1-11111-1-1-1-11111-1-1-1-100000000000000000000
χ3222222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-11111-1-1-1-11111-2-2-2-22222-2-22211111111-1-1-1-1-1-1-1-1-1-1-1-1111100000000000000000000
χ3322222222-2-2-2-2-1-2-2-22222-2-1-1-1-1-1-1-111111111-1-1-1-1002-2-22000000−i3−i3i3i3-1-11111-1-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ3422222222-2-2-2-2-1-2-2-22222-2-1-1-1-1-1-1-111111111-1-1-1-1002-2-22000000i3i3−i3−i3-1-11111-1-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ3522222222-2-2-2-2-1-2-2-22222-2-1-1-1-1-1-1-111111111-1-1-1-100-222-2000000−i3−i3i3i311-1-1-1-111i3i3−i3−i3i3i3−i3−i3−i3−i3i3i300000000000000000000
χ3622222222-2-2-2-2-1-2-2-22222-2-1-1-1-1-1-1-111111111-1-1-1-100-222-2000000i3i3−i3−i311-1-1-1-111−i3−i3i3i3−i3−i3i3i3i3i3−i3−i300000000000000000000
χ3722-2-2-222-222-2-2222-222-2-2-22-2-2-2-22222-2-222-2-222-2-20000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ3822-2-2-222-222-2-2222-222-2-2-22-2-2-2-22222-2-222-2-222-2-2000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ3922-2-2-222-222-2-22-2-22-2-22222-2-2-2-22222-2-2-2-222-2-222000000000000000000000000000000000000000000002-22-200000000
χ4022-2-2-222-222-2-22-2-22-2-22222-2-2-2-22222-2-2-2-222-2-22200000000000000000000000000000000000000000000-22-2200000000
χ4122-2-2-222-2-2-222222-2-2-222-22-2-2-2-222-2-22222-2-2-2-2220000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ4222-2-2-222-2-2-222222-2-2-222-22-2-2-2-222-2-22222-2-2-2-222000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ4322-2-2-222-2-2-2222-2-2222-2-222-2-2-2-222-2-222-2-22222-2-2000000000000000000000000000000000000000000002-2-2200000000
χ4422-2-2-222-2-2-2222-2-2222-2-222-2-2-2-222-2-222-2-22222-2-200000000000000000000000000000000000000000000-222-200000000
χ452-22-2-2-2222-22-222-222-22-2-2-222-2-22-22-22-22-22-22-22-20000002i−2i2i−2i0000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000000000
χ462-22-2-2-2222-22-222-222-22-2-2-222-2-22-22-22-22-22-22-22-2000000−2i2i−2i2i000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000000000
χ472-22-2-2-2222-22-22-22-2-22-222-222-2-22-22-22-2-22-22-22-222-2000000002-22-22-2000000002-22-20000000000000000000000000000
χ482-22-2-2-2222-22-22-22-2-22-222-222-2-22-22-22-2-22-22-22-22-2200000000-22-22-2200000000-22-220000000000000000000000000000
χ492-22-2-2-2222-22-2-12-222-22-2-21-1-111-11-11-11-11-11-11-110000002i−2i2i−2i00−i3i3i3−i33−33−33−33−3−i3i3i3−i3−ii−ii−ii−ii00000000000000000000
χ502-22-2-2-2222-22-2-12-222-22-2-21-1-111-11-11-11-11-11-11-110000002i−2i2i−2i00i3−i3−i3i3−33−33−33−33i3−i3−i3i3−ii−ii−ii−ii00000000000000000000
χ512-22-2-2-2222-22-2-12-222-22-2-21-1-111-11-11-11-11-11-11-11000000−2i2i−2i2i00−i3i3i3−i3−33−33−33−33−i3i3i3−i3i−ii−ii−ii−i00000000000000000000
χ522-22-2-2-2222-22-2-12-222-22-2-21-1-111-11-11-11-11-11-11-11000000−2i2i−2i2i00i3−i3−i3i33−33−33−33−3i3−i3−i3i3i−ii−ii−ii−i00000000000000000000
χ532-22-2-2-2222-22-2-1-22-2-22-2221-1-111-11-11-111-11-11-11-12-2000000002-2-11-113−3−333−3−33-11-113−3−333−3−3300000000000000000000
χ542-22-2-2-2222-22-2-1-22-2-22-2221-1-111-11-11-111-11-11-11-12-2000000002-2-11-11−333−3−333−3-11-11−333−3−333−300000000000000000000
χ552-22-2-2-2222-22-2-1-22-2-22-2221-1-111-11-11-111-11-11-11-1-2200000000-221-11-13−3−333−3−331-11-1−333−3−333−300000000000000000000
χ562-22-2-2-2222-22-2-1-22-2-22-2221-1-111-11-11-111-11-11-11-1-2200000000-221-11-1−333−3−333−31-11-13−3−333−3−3300000000000000000000
χ572-22-2-2-222-22-2222-22-22-22-2-222-2-22-2-22-222-22-2-22-220000002i−2i−2i2i0000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000000000
χ582-22-2-2-222-22-2222-22-22-22-2-222-2-22-2-22-222-22-2-22-22000000−2i2i2i−2i000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ592-22-2-2-222-22-222-22-22-22-22-222-2-22-2-22-22-22-222-22-22-200000000-222-22-200000000-22-220000000000000000000000000000
χ602-22-2-2-222-22-222-22-22-22-22-222-2-22-2-22-22-22-222-22-2-22000000002-2-22-22000000002-22-20000000000000000000000000000
χ612-22-2-2-222-22-22-12-22-22-22-21-1-111-111-11-1-11-111-11-10000002i−2i−2i2i00−i3i3i3−i33−33−3−33−33i3−i3−i3i3−ii−iii−ii−i00000000000000000000
χ622-22-2-2-222-22-22-12-22-22-22-21-1-111-111-11-1-11-111-11-10000002i−2i−2i2i00i3−i3−i3i3−33−333−33−3−i3i3i3−i3−ii−iii−ii−i00000000000000000000
χ632-22-2-2-222-22-22-12-22-22-22-21-1-111-111-11-1-11-111-11-1000000−2i2i2i−2i00−i3i3i3−i3−33−333−33−3i3−i3−i3i3i−ii−i−ii−ii00000000000000000000
χ642-22-2-2-222-22-22-12-22-22-22-21-1-111-111-11-1-11-111-11-1000000−2i2i2i−2i00i3−i3−i3i33−33−3−33−33−i3i3i3−i3i−ii−i−ii−ii00000000000000000000
χ652-22-2-2-222-22-22-1-22-22-22-221-1-111-111-11-11-11-1-11-112-200000000-22-11-113−3−33−333−31-11-13−3−33−333−300000000000000000000
χ662-22-2-2-222-22-22-1-22-22-22-221-1-111-111-11-11-11-1-11-112-200000000-22-11-11−333−33−3−331-11-1−333−33−3−3300000000000000000000
χ672-22-2-2-222-22-22-1-22-22-22-221-1-111-111-11-11-11-1-11-11-22000000002-21-11-13−3−33−333−3-11-11−333−33−3−3300000000000000000000
χ682-22-2-2-222-22-22-1-22-22-22-221-1-111-111-11-11-11-1-11-11-22000000002-21-11-1−333−33−3−33-11-113−3−33−333−300000000000000000000
χ692-2-222-22-22-2-2222-2-22-2-222-2-2-2222-22-2-222-2-222-2-2200000000000000000000000000000000000022-2-222-2-2000000000000
χ702-2-222-22-22-2-2222-2-22-2-222-2-2-2222-22-2-222-2-222-2-22000000000000000000000000000000000000-2-222-2-222000000000000
χ712-2-222-22-22-2-222-222-222-2-2-2-2-2222-22-2-22-222-2-222-200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ722-2-222-22-22-2-222-222-222-2-2-2-2-2222-22-2-22-222-2-222-20000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ732-2-222-22-2-222-222-2-2-222-22-2-2-2222-2-222-22-2-22-222-200000000000000000000000000000000000022-2-2-2-222000000000000
χ742-2-222-22-2-222-222-2-2-222-22-2-2-2222-2-222-22-2-22-222-2000000000000000000000000000000000000-2-22222-2-2000000000000
χ752-2-222-22-2-222-22-2222-2-22-2-2-2-2222-2-222-2-222-22-2-2200000000000000000000000000000000000000000000000000002i−2i−2i2i
χ762-2-222-22-2-222-22-2222-2-22-2-2-2-2222-2-222-2-222-22-2-220000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ774444-4-4-4-4000040000000044-44-4-4-400000000000000000000000000000000000000000000000022−2222−220000000000000000
χ784444-4-4-4-4000040000000044-44-4-4-4000000000000000000000000000000000000000000000000−2222−22220000000000000000
χ7944-4-44-4-4400004000000004-44-44-4-40000000000000000000000000000000000000000000000000000−2i22i2−2i22i2000000000000
χ8044-4-44-4-4400004000000004-44-44-4-400000000000000000000000000000000000000000000000000002i2−2i22i2−2i2000000000000
χ8144-4-4-444-444-4-4-244-444-4-4-4-22222-2-2-2-222-2-222-2-22200000000000000000000000000000000000000000000000000000000
χ8244-4-4-444-444-4-4-2-4-44-4-4444-22222-2-2-2-22222-2-222-2-200000000000000000000000000000000000000000000000000000000
χ8344-4-4-444-4-4-444-244-4-4-444-4-22222-2-222-2-2-2-22222-2-200000000000000000000000000000000000000000000000000000000
χ8444-4-4-444-4-4-444-2-4-4444-4-44-22222-2-222-2-222-2-2-2-22200000000000000000000000000000000000000000000000000000000
χ854-44-444-4-40000400000000-44-4-44-440000000000000000000000000000000000000000000000000000−2i22i22i2−2i2000000000000
χ864-44-444-4-40000400000000-44-4-44-4400000000000000000000000000000000000000000000000000002i2−2i2−2i22i2000000000000
χ874-4-444-44-44-4-44-24-4-44-4-444222-2-2-22-222-2-222-2-222-200000000000000000000000000000000000000000000000000000000
χ884-4-444-44-44-4-44-2-444-444-4-4222-2-2-22-222-22-2-222-2-2200000000000000000000000000000000000000000000000000000000
χ894-4-444-44-4-444-4-24-4-4-444-44222-2-2-222-2-22-222-22-2-2200000000000000000000000000000000000000000000000000000000
χ904-4-444-44-4-444-4-2-4444-4-44-4222-2-2-222-2-222-2-22-222-200000000000000000000000000000000000000000000000000000000
χ914-4-44-44-440000400000000-4-444-4-4400000000000000000000000000000000000000000000000022−22−22220000000000000000
χ924-4-44-44-440000400000000-4-444-4-44000000000000000000000000000000000000000000000000−222222−220000000000000000
χ938888-8-8-8-80000-400000000-4-44-444400000000000000000000000000000000000000000000000000000000000000000000
χ9488-8-88-8-880000-400000000-44-44-44400000000000000000000000000000000000000000000000000000000000000000000
χ958-88-888-8-80000-4000000004-444-44-400000000000000000000000000000000000000000000000000000000000000000000
χ968-8-88-88-880000-40000000044-4-444-400000000000000000000000000000000000000000000000000000000000000000000

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