Finite Group Databasebeta

← Group #10706822

Character table — Group #10706822

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11112222222222222222222222222244444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order122234444444444666888888881212121224668888121212121212121212122424242424242424242424242424242416161616161616161616161616161616888824242424242424248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−iii−i−i
χ611111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii−i−iii
χ711111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−iiiii−i−i−i−i−i−iii
χ811111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iii−i−i−i−iiiiiii−i−i
χ911111-1-1-1-1111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-111-1-111-1-11-11-1
χ1011111-1-1-1-1111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-11-11
χ1111111-1-1-1-1111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-111-1-111-1-1-11-11
χ1211111-1-1-1-1111111111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11-1-111-1-1111-11-1
χ1311111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111i−i−iiii−i−i−i−iiii−i−ii
χ1411111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−iii−i−i−iiiii−i−i−iii−i
χ1511111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1i−i−iiii−i−i−i−iii−iii−i
χ1611111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1−iii−i−i−iiiii−i−ii−i−ii
χ17222222222222222222-2-2-2-2-2-2-2-222222222-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000
χ1822222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-222-2-2-2-2-2-2-2-22222222200000000000000000000000000000000
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χ202222222-2-2-2-222-2-22220000000022222-222000022-2-2-2-2-2-2-2-20000000000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000
χ212222222-2-2-2-2-2-22222200000000-2-2-2-2-22-2-2000022-2-22222-2-20000000000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000
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χ2322222-2-222-2-222-2-2222000000002222-22-2-20000-2-222-2-222-2-20000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000000000
χ2422222-2-222-2-222-2-2222000000002222-22-2-20000-2-222-2-222-2-20000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000000000
χ2522222-2-222-2-2-2-22222200000000-2-2-2-22-2220000-2-22222-2-2-2-20000000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000000000
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χ2722222-2-2-2-22222222222222-2-2-2-22222-2-2-2-2-2-222-2-2-2-222-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2822222-2-2-2-222-2-2-2-22222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ292222-12222222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ302222-12222222222-1-1-122222222-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ312222-12222222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ322222-12222222222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ332222-1222222-2-2-2-2-1-1-1222222221111-2-211-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111100000000000000002i2i−2i−2i−i−i−i−iiiii0000
χ342222-1222222-2-2-2-2-1-1-1222222221111-2-211-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111110000000000000000−2i−2i2i2iiiii−i−i−i−i0000
χ352222-1222222-2-2-2-2-1-1-1-2-2-2-2-2-2-2-21111-2-2112222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1000000000000000000003−33−3−33−330000
χ362222-1222222-2-2-2-2-1-1-1-2-2-2-2-2-2-2-21111-2-2112222-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-100000000000000000000−33−333−33−30000
χ372222-1-2-2-2-2222222-1-1-12222-2-2-2-2-1-1-1-1-2-211-2-2221111-1-111-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3i3−i3−i3i3i3−i30000
χ382222-1-2-2-2-2222222-1-1-12222-2-2-2-2-1-1-1-1-2-211-2-2221111-1-111-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3−i3i3i3−i3−i3i30000
χ392222-1-2-2-2-2222222-1-1-1-2-2-2-22222-1-1-1-1-2-21122-2-21111-1-111-1-1-1-1-1-11111-1-1-1-1111100000000000000002-22-2-1-111-1-1110000
χ402222-1-2-2-2-2222222-1-1-1-2-2-2-22222-1-1-1-1-2-21122-2-21111-1-111-1-1-1-1-1-11111-1-1-1-111110000000000000000-22-2211-1-111-1-10000
χ412222-1-2-2-2-222-2-2-2-2-1-1-12222-2-2-2-2111122-1-122-2-2111111-1-1-1-11111-1-1-1-1-1-1-1-11111000000000000000000003−3−33−333−30000
χ422222-1-2-2-2-222-2-2-2-2-1-1-12222-2-2-2-2111122-1-122-2-2111111-1-1-1-11111-1-1-1-1-1-1-1-1111100000000000000000000−333−33−3−330000
χ432222-1-2-2-2-222-2-2-2-2-1-1-1-2-2-2-22222111122-1-1-2-222111111-1-1-1-1-1-1-1-111111111-1-1-1-100000000000000002i−2i−2i2i−i−iiiii−i−i0000
χ442222-1-2-2-2-222-2-2-2-2-1-1-1-2-2-2-22222111122-1-1-2-222111111-1-1-1-1-1-1-1-111111111-1-1-1-10000000000000000−2i2i2i−2iii−i−i−i−iii0000
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χ904-4-44-24-40000000022-2−2i22i22i2−2i2−2i22i22i2−2i22i3−2i3−2i32i3002i3−2i30000-2200000000i2−i2−i2i2i2−i2−i2i2−666−6−666−600000000000000000000000000000000
χ914-4-44-24-40000000022-22i2−2i2−2i22i22i2−2i2−2i22i2−2i32i32i3−2i300−2i32i30000-2200000000−i2i2i2−i2−i2i2i2−i2−666−6−666−600000000000000000000000000000000
χ924-4-44-24-40000000022-22i2−2i2−2i22i22i2−2i2−2i22i22i3−2i3−2i32i3002i3−2i30000-2200000000−i2i2i2−i2−i2i2i2−i26−6−666−6−6600000000000000000000000000000000
χ934-4-44-2-440000000022-2−2i22i22i2−2i22i2−2i2−2i22i2−2i32i32i3−2i3002i3−2i300002-200000000−i2i2i2−i2i2−i2−i2i2−666−66−6−6600000000000000000000000000000000
χ944-4-44-2-440000000022-2−2i22i22i2−2i22i2−2i2−2i22i22i3−2i3−2i32i300−2i32i300002-200000000−i2i2i2−i2i2−i2−i2i26−6−66−666−600000000000000000000000000000000
χ954-4-44-2-440000000022-22i2−2i2−2i22i2−2i22i22i2−2i2−2i32i32i3−2i3002i3−2i300002-200000000i2−i2−i2i2−i2i2i2−i26−6−66−666−600000000000000000000000000000000
χ964-4-44-2-440000000022-22i2−2i2−2i22i2−2i22i22i2−2i22i3−2i3−2i32i300−2i32i300002-200000000i2−i2−i2i2−i2i2i2−i2−666−66−6−6600000000000000000000000000000000

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