Finite Group Databasebeta

← Group #10823193

Character table — Group #10823193

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order12222222222234444444466666661212121212121212444444446666121212121212121212121212121212121212121288888888242424242424242424242424242424242222224444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-1-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1111111
χ911111111-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1
χ1011111111-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1-111
χ1111111111-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1111111-1-1
χ1211111111-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-1-1-111
χ1311111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-111-1-1-1-111
χ1411111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-1
χ1511111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111-1-111
χ1611111111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-111-1-1
χ172222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-222-2-222-2-22222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ19222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ20222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ21222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ22222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ23222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-111110000000033−3−333−3−333−3−333−3−30000000000000000
χ24222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000−3−333−3−333−3−333−3−3330000000000000000
χ25222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-2-222-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-10000000033−3−333−3−3−3−333−3−3330000000000000000
χ26222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-111111111-2-222-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-100000000−3−333−3−33333−3−333−3−30000000000000000
χ2722222222-2-2-2-22-2-2-22222-22222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2-2-222222222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ2822222222-2-2-2-22-2-2-22222-22222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ2922222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ3022222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-211111111-1-1-1-1-1-1-1-111111111-2-222-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ3122222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ3222222222-2-2-2-2-1222-2-2-2-22-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222221111111111111111-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ3322222222-2-2-2-2-1-2-2-22222-2-1-1-1-1-1-1-11111111122-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-10000000033−3−3−3−33333−3−3−3−3330000000000000000
χ3422222222-2-2-2-2-1-2-2-22222-2-1-1-1-1-1-1-11111111122-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000−3−33333−3−3−3−33333−3−30000000000000000
χ3522222222-2-2-2-2-1-2-2-22222-2-1-1-1-1-1-1-111111111-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-111110000000033−3−3−3−333−3−33333−3−30000000000000000
χ3622222222-2-2-2-2-1-2-2-22222-2-1-1-1-1-1-1-111111111-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000−3−33333−3−333−3−3−3−3330000000000000000
χ3722-2-2-2-22222-2-2222-222-2-2-222-2-22-2-22222-2-2-2-20000000022-2-222-2-200000000000000000000000000000000000000000000002i−2i2i−2i000000
χ3822-2-2-2-22222-2-2222-222-2-2-222-2-22-2-22222-2-2-2-20000000022-2-222-2-20000000000000000000000000000000000000000000000−2i2i−2i2i000000
χ3922-2-2-2-22222-2-22-2-22-2-222222-2-22-2-2-2-2-2-222220000000022-2-2-2-222000000000000000000000000000000000000000000002-200002-20000
χ4022-2-2-2-22222-2-22-2-22-2-222222-2-22-2-2-2-2-2-222220000000022-2-2-2-22200000000000000000000000000000000000000000000-220000-220000
χ4122-2-2-2-222-2-222222-2-2-222-222-2-22-2-22222-2-2-2-200000000-2-222-2-22200000000000000000000000000000000000000000000002i−2i−2i2i000000
χ4222-2-2-2-222-2-222222-2-2-222-222-2-22-2-22222-2-2-2-200000000-2-222-2-2220000000000000000000000000000000000000000000000−2i2i2i−2i000000
χ4322-2-2-2-222-2-2222-2-2222-2-2222-2-22-2-2-2-2-2-2222200000000-2-22222-2-2000000000000000000000000000000000000000000002-20000-220000
χ4422-2-2-2-222-2-2222-2-2222-2-2222-2-22-2-2-2-2-2-2222200000000-2-22222-2-200000000000000000000000000000000000000000000-2200002-20000
χ452-222-2-22-22-22-222-222-22-2-2-2-2-2-222222-2-222-2-2000000002-22-22-22-2000000000000000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ462-222-2-22-22-22-222-222-22-2-2-2-2-2-222222-2-222-2-2000000002-22-22-22-200000000000000000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i0000000000000000
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χ482-222-2-22-22-22-22-22-2-22-222-2-2-2-2222-2-222-2-222000000002-22-2-22-220000000000000000-22-220000-22-22-22-22000000000000000000000000
χ492-222-2-22-22-22-2-12-222-22-2-21111-1-1-1-1-111-1-11100000000-11-11-11-11−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300002i−2i2i−2i3−3−333−3−33−ii−ii−ii−ii0000000000000000
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χ582-222-2-22-2-22-2222-22-22-22-2-2-2-2-222222-2-222-2-200000000-22-22-22-2200000000000000000000−2i2i2i−2i00000000−2i2i−2i2i2i−2i2i−2i0000000000000000
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χ8944-4-4-4-44444-4-4-244-444-4-4-4-2-222-222-2-2-2-2222200000000-2-222-2-22200000000000000000000000000000000000000000000000000000000
χ9044-4-4-4-44444-4-4-2-4-44-4-4444-2-222-2222222-2-2-2-200000000-2-22222-2-200000000000000000000000000000000000000000000000000000000
χ9144-4-4-4-444-4-444-244-4-4-444-4-2-222-222-2-2-2-222220000000022-2-222-2-200000000000000000000000000000000000000000000000000000000
χ9244-4-4-4-444-4-444-2-4-4444-4-44-2-222-2222222-2-2-2-20000000022-2-2-2-22200000000000000000000000000000000000000000000000000000000
χ934-44-4-44-440000400000000-44-44-44-40000000000004-40000000000000000004-4-4400000000000000000000000000000000000000000000
χ944-44-4-44-440000400000000-44-44-44-4000000000000-44000000000000000000-444-400000000000000000000000000000000000000000000
χ954-44-4-44-440000-2000000002-22-22-2223−23−232323−23−232300004-4000000000000000000-222-223−23−23230000000000000000000000000000000000000000
χ964-44-4-44-440000-2000000002-22-22-2223−23−232323−23−23230000-440000000000000000002-2-22−232323−230000000000000000000000000000000000000000
χ974-44-4-44-440000-2000000002-22-22-22−232323−23−232323−2300004-4000000000000000000-222-2−232323−230000000000000000000000000000000000000000
χ984-44-4-44-440000-2000000002-22-22-22−232323−23−232323−230000-440000000000000000002-2-2223−23−23230000000000000000000000000000000000000000
χ994-4-444-4-440000400000000-444-4-4-4400000000004-400000000000000004-4-44000000000000000000000000000000000000000000000000
χ1004-4-444-4-440000400000000-444-4-4-440000000000-440000000000000000-444-4000000000000000000000000000000000000000000000000
χ1014-4-444-4-440000-2000000002-2-2222-223−23−2323−232323−23004-400000000000023−23−2323-222-2000000000000000000000000000000000000000000000000
χ1024-4-444-4-440000-2000000002-2-2222-223−23−2323−232323−2300-44000000000000−232323−232-2-22000000000000000000000000000000000000000000000000
χ1034-4-444-4-440000-2000000002-2-2222-2−232323−2323−23−2323004-4000000000000−232323−23-222-2000000000000000000000000000000000000000000000000
χ1044-4-444-4-440000-2000000002-2-2222-2−232323−2323−23−232300-4400000000000023−23−23232-2-22000000000000000000000000000000000000000000000000
χ1054-4-4-4444-44-4-44-24-4-44-4-44422-2-2-222-2-22222-2-200000000-222-2-222-200000000000000000000000000000000000000000000000000000000
χ1064-4-4-4444-44-4-44-2-444-444-4-422-2-2-22222-2-2-2-22200000000-222-22-2-2200000000000000000000000000000000000000000000000000000000
χ1074-4-4-4444-4-444-4-24-4-4-444-4422-2-2-222-2-22222-2-2000000002-2-222-2-2200000000000000000000000000000000000000000000000000000000
χ1084-4-4-4444-4-444-4-2-4444-4-44-422-2-2-22222-2-2-2-222000000002-2-22-222-200000000000000000000000000000000000000000000000000000000

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