Finite Group Databasebeta

← Group #10823633

Character table — Group #10823633

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444448888888888888888888888888888888888881212121212121212242424242424242424242424
order1222444422344444444446661212121266121212121212121212122244444444446666121212121212121212121212121212121212121244444444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-11-111-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111-11-111-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111111111111111-11-11-1-111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111111111111111-11-11-1-111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ91111-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-111-1-11-11-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ101111-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-111-1-11-11-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ111111-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-11-1-111-1-11-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ121111-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-11-1-111-1-11-1-11111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1
χ131111-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-111-1-111-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1
χ141111-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-111-1-111-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ151111-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-1-111-11-1111-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111
χ161111-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-1-111-11-1111-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1
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
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
χ202222222222-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-22-222-2-2-2-2-2-2-1-111-1-111-1-1-1-111111111111100000000000000000000
χ212222222222-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-22-22-2-222-2-2-2-211-1-111-1-11111-1-1-1-11111111100000000000000000000
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
χ232222222222-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-111111111000000002-22-2−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3-1-111-1-11100000000000000000000
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χ252222222222-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-11111111100000000-22-22−i3i3i3−i3−i3i3i3−i3−i3i3−i3i3i3−i3i3−i311-1-111-1-100000000000000000000
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χ2722222222-2-22-2-222-2-222-2-22222222-2-2-2-222-2-222-2-2020200-2-20000002200220000-2-2-2-20000000000000000000000000000
χ2822222222-2-22-2-222-2-222-2-22222222-2-2-2-222-2-222-2-20-20-20022000000-2-200-2-2000022220000000000000000000000000000
χ2922222222-2-22-2-2-2-222-2-2222222222-2-2-2-2-2-222-2-2222020-2-200000022002200-2-2-2-200000000000000000000000000000000
χ3022222222-2-22-2-2-2-222-2-2222222222-2-2-2-2-2-222-2-222-20-2022000000-2-200-2-200222200000000000000000000000000000000
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χ3322222222-2-2-1-2-222-2-222-2-2-1-1-1-1-1-1-11111-1-111-1-1110-20-200220000−i3i311−i3i311i3−i3i3−i3-1-1-1-1i3−i3i3−i3i3−i3i3−i300000000000000000000
χ3422222222-2-2-1-2-222-2-222-2-2-1-1-1-1-1-1-11111-1-111-1-1110-20-200220000i3−i311i3−i311−i3i3−i3i3-1-1-1-1−i3i3−i3i3−i3i3−i3i300000000000000000000
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χ442222-2-2-2-222-1-2-22222-2-2-2-2-1-1-11111-1-1111111-1-1-1-100000000-222-2i3−i3−i3i3−i3i3i3−i3i3−i3−i3i3−i3i3i3−i311-1-1-1-11100000000000000000000
χ452222-2-2-2-222-1-2-2-2-2-2-22222-1-1-11111-1-111-1-1-1-1111122-2-22-22-222-2-2-1-1-1-11111-1-111-1-111-1-1-1-1111100000000000000000000
χ462222-2-2-2-222-1-2-2-2-2-2-22222-1-1-11111-1-111-1-1-1-111112-2-222-2-22-2-222-1-11111-1-1-1-11111-1-11111-1-1-1-100000000000000000000
χ472222-2-2-2-222-1-2-2-2-2-2-22222-1-1-11111-1-111-1-1-1-11111-222-2-222-2-2-22211-1-1-1-11111-1-1-1-1111111-1-1-1-100000000000000000000
χ482222-2-2-2-222-1-2-2-2-2-2-22222-1-1-11111-1-111-1-1-1-11111-2-222-22-2222-2-21111-1-1-1-111-1-111-1-1-1-1-1-1111100000000000000000000
χ492222-2-2-2-2-2-222222-2-2-2-222222-2-2-2-2-2-222-2-22222-2-220-20-220000002200-2-200-2-22200000000000000000000000000000000
χ502222-2-2-2-2-2-222222-2-2-2-222222-2-2-2-2-2-222-2-22222-2-2-20202-2000000-2-200220022-2-200000000000000000000000000000000
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χ522222-2-2-2-2-2-2222-2-22222-2-2222-2-2-2-2-2-22222-2-2-2-2220-202002-2000000-2-20022000022-2-20000000000000000000000000000
χ532222-2-2-2-2-2-2-12222-2-2-2-222-1-1-1111111-1-111-1-1-1-11120-20-22000000-1-1−i3i311i3−i311-1-1i3−i3−i3i3−i3i3i3−i3i3−i3−i3i300000000000000000000
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χ562222-2-2-2-2-2-2-12222-2-2-2-222-1-1-1111111-1-111-1-1-1-111-20202-200000011i3−i3-1-1−i3i3-1-111−i3i3i3−i3−i3i3i3−i3i3−i3−i3i300000000000000000000
χ572222-2-2-2-2-2-2-122-2-22222-2-2-1-1-1111111-1-1-1-11111-1-1020-200-220000−i3i3-1-1i3−i311i3−i3−i3i311-1-1−i3i3−i3i3i3−i3i3−i300000000000000000000
χ582222-2-2-2-2-2-2-122-2-22222-2-2-1-1-1111111-1-1-1-11111-1-1020-200-220000i3−i3-1-1−i3i311−i3i3i3−i311-1-1i3−i3i3−i3−i3i3−i3i300000000000000000000
χ592222-2-2-2-2-2-2-122-2-22222-2-2-1-1-1111111-1-1-1-11111-1-10-202002-20000−i3i311i3−i3-1-1i3−i3−i3i3-1-111i3−i3i3−i3−i3i3−i3i300000000000000000000
χ602222-2-2-2-2-2-2-122-2-22222-2-2-1-1-1111111-1-1-1-11111-1-10-202002-20000i3−i311−i3i3-1-1−i3i3i3−i3-1-111−i3i3−i3i3i3−i3i3−i300000000000000000000
χ612-22-22i2i−2i−2i2-222i−2i2i−2i2i−2i2-22-2-22-22i2i−2i−2i2-22i−2i2-22-22i−2i2i−2i00000000000000000000000000000000000000000000000000002-22i−2i
χ622-22-22i2i−2i−2i2-222i−2i2i−2i2i−2i2-22-2-22-22i2i−2i−2i2-22i−2i2-22-22i−2i2i−2i0000000000000000000000000000000000000000000000000000-22−2i2i
χ632-22-22i2i−2i−2i2-222i−2i−2i2i−2i2i-22-22-22-22i2i−2i−2i2-22i−2i-22-22−2i2i−2i2i0000000000000000000000000000000000000000000000002-22i−2i0000
χ642-22-22i2i−2i−2i2-222i−2i−2i2i−2i2i-22-22-22-22i2i−2i−2i2-22i−2i-22-22−2i2i−2i2i000000000000000000000000000000000000000000000000-22−2i2i0000
χ652-22-22i2i−2i−2i-222−2i2i2i−2i−2i2i2-2-22-22-22i2i−2i−2i-22−2i2i2-2-222i−2i−2i2i0000000000000000000000000000000000002i2i−2i−2i22-2-2000000000000
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χ958-8-888i−8i−8i8i00-4000000000044-4−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ968-8-88−8i8i8i−8i00-4000000000044-44i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000

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