Finite Group Databasebeta

← Group #10824893

Character table — Group #10824893

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order12224444223444444444466612121212661212121212121212121244448888888812121212121212122424242424242424242424242424242488888888222444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-111-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111111
χ51111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1111-1-11-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-11111
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
χ91111-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ101111-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111
χ111111-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-11-1-11-1-111
χ121111-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-111-111-1-1
χ131111-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-111-1-1-111
χ141111-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11-1-1111-1-1
χ151111-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ161111-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ1722222222222-2-2-2-222-2-2-2-222222222222-2-2-2-2-2-2-2-200002i−2i2i−2i0000000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ1822222222222-2-2-2-222-2-2-2-222222222222-2-2-2-2-2-2-2-20000−2i2i−2i2i000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ192222222222-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ202222222222-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000000000000000
χ212222222222-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000000000000000
χ222222222222-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000000000000000
χ232222222222-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111100002i−2i2i−2i0000−i3−i3i3i3−i3−i3i3i3−i−iii−i−iii33−3−333−3−300000000000000000000
χ242222222222-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111100002i−2i2i−2i0000i3i3−i3−i3i3i3−i3−i3−i−iii−i−iii−3−333−3−33300000000000000000000
χ252222222222-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111110000−2i2i−2i2i0000−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i−3−333−3−33300000000000000000000
χ262222222222-1-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1111111110000−2i2i−2i2i0000i3i3−i3−i3i3i3−i3−i3ii−i−iii−i−i33−3−333−3−300000000000000000000
χ2722222222-2-2222-2-2-2-222-2-22222222-2-2-2-222-2-222-2-200000000000000000000000000000000000022-2-222-2-2000000000000
χ2822222222-2-2222-2-2-2-222-2-22222222-2-2-2-222-2-222-2-2000000000000000000000000000000000000-2-222-2-222000000000000
χ2922222222-2-22-2-222-2-2-2-2222222222-2-2-2-2-2-222-2-22200000000000000000000000000000000000000000000002-2-20020000
χ3022222222-2-22-2-222-2-2-2-2222222222-2-2-2-2-2-222-2-2220000000000000000000000000000000000000000000000-22200-20000
χ312222-2-2-2-22222222-2-2-2-2-2-2222-2-2-2-222-2-22222-2-2-2-200002i−2i−2i2i0000000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ322222-2-2-2-22222222-2-2-2-2-2-2222-2-2-2-222-2-22222-2-2-2-20000−2i2i2i−2i000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ332222-2-2-2-222-12222-2-2-2-2-2-2-1-1-11111-1-111-1-1-1-1111100002i−2i−2i2i0000−i3−i3i3i3i3i3−i3−i3−i−iiiii−i−i33−3−3−3−33300000000000000000000
χ342222-2-2-2-222-12222-2-2-2-2-2-2-1-1-11111-1-111-1-1-1-1111100002i−2i−2i2i0000i3i3−i3−i3−i3−i3i3i3−i−iiiii−i−i−3−33333−3−300000000000000000000
χ352222-2-2-2-222-12222-2-2-2-2-2-2-1-1-11111-1-111-1-1-1-111110000−2i2i2i−2i0000−i3−i3i3i3i3i3−i3−i3ii−i−i−i−iii−3−33333−3−300000000000000000000
χ362222-2-2-2-222-12222-2-2-2-2-2-2-1-1-11111-1-111-1-1-1-111110000−2i2i2i−2i0000i3i3−i3−i3−i3−i3i3i3ii−i−i−i−iii33−3−3−3−33300000000000000000000
χ372222-2-2-2-222-1-2-2-2-2-2-22222-1-1-11111-1-1111111-1-1-1-122-2-222-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111100000000000000000000
χ382222-2-2-2-222-1-2-2-2-2-2-22222-1-1-11111-1-1111111-1-1-1-122-2-2-2-222-2-222-1-1-1-111111111-1-1-1-11111-1-1-1-100000000000000000000
χ392222-2-2-2-222-1-2-2-2-2-2-22222-1-1-11111-1-1111111-1-1-1-1-2-22222-2-2-2-2221111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000000000
χ402222-2-2-2-222-1-2-2-2-2-2-22222-1-1-11111-1-1111111-1-1-1-1-2-222-2-22222-2-21111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000
χ412222-2-2-2-2-2-2222-2-222-2-222222-2-2-2-2-2-22222-2-2-2-22200000000000000000000000000000000000000000000002-2200-20000
χ422222-2-2-2-2-2-2222-2-222-2-222222-2-2-2-2-2-22222-2-2-2-2220000000000000000000000000000000000000000000000-22-20020000
χ432222-2-2-2-2-2-22-2-2222222-2-2222-2-2-2-2-2-222-2-22222-2-200000000000000000000000000000000000022-2-2-2-222000000000000
χ442222-2-2-2-2-2-22-2-2222222-2-2222-2-2-2-2-2-222-2-22222-2-2000000000000000000000000000000000000-2-22222-2-2000000000000
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χ4622-2-22i2i−2i−2i2-222i−2i2i−2i2i−2i2-22-2-22-22i2i−2i−2i2-22i−2i2i−2i2i−2i2-22-20000000000000000000000000000000000000000000000000000-22−2i2i
χ4722-2-22i2i−2i−2i2-22−2i2i−2i2i2i−2i-22-22-22-22i2i−2i−2i2-22i−2i−2i2i−2i2i-22-22000000000000000000000000000000000000000000002-20002i−2i00000
χ4822-2-22i2i−2i−2i2-22−2i2i−2i2i2i−2i-22-22-22-22i2i−2i−2i2-22i−2i−2i2i−2i2i-22-2200000000000000000000000000000000000000000000-22000−2i2i00000
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χ5222-2-22i2i−2i−2i-222−2i2i2i−2i−2i2i-222-2-22-22i2i−2i−2i-22−2i2i−2i2i2i−2i-222-2-22−2i2i00000000-22-22−2i2i−2i2i000000000000000000000000000000000000
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χ6422-2-2−2i−2i2i2i2-22−2i2i−2i2i−2i2i2-22-2-22-2−2i−2i2i2i2-2−2i2i−2i2i−2i2i2-22-20000000000000000000000000000000000000000000000000000-222i−2i
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χ924-4-44-444-400400000000004-4-4-444-40000000000000000000000000000000000000000000000002i2−2i200−2i22i200000000000000
χ938-88-88i−8i8i−8i00-4000000000044-4−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ948-88-8−8i8i−8i8i00-4000000000044-44i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ958-8-888-8-8800-40000000000-444-444-400000000000000000000000000000000000000000000000000000000000000000000
χ968-8-88-888-800-40000000000-4444-4-4400000000000000000000000000000000000000000000000000000000000000000000

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