Finite Group Databasebeta

← Group #10868063

Character table — Group #10868063

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222444444444444444444444444444444444488888888888888888888888888121212121212121224242424242424244848
order1222222234444444466666664444444444121212121212121212121212121212121212121212121212244444446612121212121212121212121212121212888888884444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ4111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111111111-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ9111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111-11
χ10111111111-1-1-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-11-1
χ11111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1111-1
χ12111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-11
χ13111111111-1-1-1-111111111111-1-111-1-111111111-1-1-1-1111111111111-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11-1
χ14111111111-1-1-1-111111111111-1-111-1-111111111-1-1-1-1111111111111-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-11
χ15111111111-1-1-1-111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-11111-1-111-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-11
χ16111111111-1-1-1-111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11-1-11111-1-111-1-1-1-1-1-111111111-1-1-1-1111111-1-1-1-1111-1
χ172222222222222-2-2-2-222222222222-2-200002222222200000000-2-2-2-22222-2-2000000-2-2-2-20000-2-200000000000000000000000000
χ182222222222222-2-2-2-22222222-2-2-2-2-2-20000-2-2-2-2222200000000-2-2-2-2-2-2-2-22200000022220000-2-200000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-2222222222-2-2220000-2-2-2-2-2-2-2-200000000-2-2-2-22222-22000000-2-22200002200000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-22222222-2-2222200002222-2-2-2-200000000-2-2-2-2-2-2-2-22-200000022-2-200002200000000000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ2222222222-122222222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-122-2-2-2-2-2-2-1-1-1-11111-1-111111111000000000000000000
χ2322222222-122222222-1-1-1-1-1-1-1-2-2-2-22222221111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-2-2-22211111111-1-11111-1-1-1-1000000000000000000
χ2422222222-122222222-1-1-1-1-1-1-1-2-2-2-222-2-2-2-21111-1-1-1-111111111-1-1-1-11111-2-22222-2-21111-1-1-1-1-1-1-1-1-1-11111000000000000000000
χ2522222222-12222-2-2-2-2-1-1-1-1-1-1-12222-2-20000-1-1-1-1-1-1-1-1−i3−i3−i3−i3i3i3i3i31111-1-1-1-1-2-20000001111−i3−i3i3i311−i3−i3i3i3−i3−i3i3i3000000000000000000
χ2622222222-12222-2-2-2-2-1-1-1-1-1-1-12222-2-20000-1-1-1-1-1-1-1-1i3i3i3i3−i3−i3−i3−i31111-1-1-1-1-2-20000001111i3i3−i3−i311i3i3−i3−i3i3i3−i3−i3000000000000000000
χ2722222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-200001111-1-1-1-1−i3−i3−i3−i3i3i3i3i31111111122000000-1-1-1-1i3i3−i3−i311i3i3−i3−i3−i3−i3i3i3000000000000000000
χ2822222222-12222-2-2-2-2-1-1-1-1-1-1-1-2-2-2-2-2-200001111-1-1-1-1i3i3i3i3−i3−i3−i3−i31111111122000000-1-1-1-1−i3−i3i3i311−i3−i3i3i3i3i3−i3−i3000000000000000000
χ2922222222-1-2-2-2-22222-1-1-1-1-1-1-122-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12-2-2-222-2-2-1-111111111-1-1-1-11111000000000000000000
χ3022222222-1-2-2-2-22222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-21111111111111111-1-1-1-1-1-1-1-12-222-2-222-1-111-1-1-1-1111111-1-1-1-1000000000000000000
χ3122222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-222-2-22222-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-2222-2-2-2-211-1-1-1-1-1-11111111111000000000000000000
χ3222222222-1-2-2-2-22222-1-1-1-1-1-1-1-2-222-2-2-2-2-2-2-1-1-1-1111111111111-1-1-1-11111-22-2-2222211-1-1111111-1-1-1-1-1-1-1-1000000000000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-222000011111111−i3−i3−i3−i3i3i3i3i31111-1-1-1-1-2200000011-1-1i3i3−i3−i3-1-1−i3−i3i3i3i3i3−i3−i3000000000000000000
χ3422222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122-2-222000011111111i3i3i3i3−i3−i3−i3−i31111-1-1-1-1-2200000011-1-1−i3−i3i3i3-1-1i3i3−i3−i3−i3−i3i3i3000000000000000000
χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-222220000-1-1-1-11111−i3−i3−i3−i3i3i3i3i3111111112-2000000-1-111−i3−i3i3i3-1-1i3i3−i3−i3i3i3−i3−i3000000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-2-222220000-1-1-1-11111i3i3i3i3−i3−i3−i3−i3111111112-2000000-1-111i3i3−i3−i3-1-1−i3−i3i3i3−i3−i3i3i3000000000000000000
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χ3822-2-222-2-220000-22-22-222-2-2-220000002i2i−2i−2i000000002i2i−2i−2i2i2i−2i−2i22-2-20000000000000000000000000000000000-2-22200−2i2i000000
χ3922-2-222-2-220000-22-22-222-2-2-22000000−2i−2i2i2i00000000−2i−2i2i2i−2i−2i2i2i22-2-2000000000000000000000000000000000022-2-200−2i2i000000
χ4022-2-222-2-220000-22-22-222-2-2-22000000−2i−2i2i2i00000000−2i−2i2i2i−2i−2i2i2i22-2-20000000000000000000000000000000000-2-222002i−2i000000
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χ422-22-22-2-2222i2i−2i−2i2-2-222-2-22-2-2200002i−2i000000002i2i−2i−2i000000002-22-2000000-22−2i2i000000-22-222i−2i−2i2i−2i2i0000000000000000000000
χ432-22-22-2-2222i2i−2i−2i-222-22-2-22-2-220000−2i2i2i−2i2i−2i00002i2i−2i−2i2i−2i2i−2i2i−2i2i−2i-22-2200000000002-200000000−2i2i00002-22-2000000000000000000
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χ472-22-22-2-222−2i−2i2i2i-222-22-2-22-2-2200002i−2i2i−2i2i−2i0000−2i−2i2i2i2i−2i2i−2i2i−2i2i−2i-22-220000000000-22000000002i−2i0000-22-22000000000000000000
χ482-22-22-2-222−2i−2i2i2i-222-22-2-22-2-2200002i−2i−2i2i−2i2i0000−2i−2i2i2i−2i2i−2i2i−2i2i−2i2i-22-2200000000002-2000000002i−2i00002-22-2000000000000000000
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χ522-22-22-2-22-12i2i−2i−2i2-2-22-111-111-100002i−2i0000−3−333−i−iii−33−333−33−3-11-11i3i3−i3−i3002-22i−2i00i3−i3−33-11-11−ii−ii−iii3−i3−i3i3000000000000000000
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χ8644-4-444-4-4-20000-44-442-2-2222-20000004i4i−4i−4i00000000−2i−2i2i2i−2i−2i2i2i-2-222000000000000000000000000000000000000000000000000
χ8744-4-444-4-4-20000-44-442-2-2222-2000000−4i−4i4i4i000000002i2i−2i−2i2i2i−2i−2i-2-222000000000000000000000000000000000000000000000000
χ8844-4-4-4-4444000000004-44-44-4-4000000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i200000000000000
χ8944-4-4-4-4444000000004-44-44-4-40000000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i200000000000000
χ904-44-4-444-4-24i−4i4i−4i00002-22-2-2224i−4i4-4000000-22-22−2i2i−2i2i000000000000−2i2i−2i2i00000000000000000000000000000000000000000000
χ914-44-4-444-4-24i−4i4i−4i00002-22-2-222−4i4i-440000002-22-2−2i2i−2i2i0000000000002i−2i2i−2i00000000000000000000000000000000000000000000
χ924-44-4-444-4-2−4i4i−4i4i00002-22-2-2224i−4i-440000002-22-22i−2i2i−2i000000000000−2i2i−2i2i00000000000000000000000000000000000000000000
χ934-44-4-444-4-2−4i4i−4i4i00002-22-2-222−4i4i4-4000000-22-222i−2i2i−2i0000000000002i−2i2i−2i00000000000000000000000000000000000000000000
χ944-4-444-44-440000-4-444-4-4-4-4444000000000000000000000000004-4-44000000000000000000000000000000000000000000000000
χ954-4-444-44-4-2000044-4-42222-2-2-20000004-4-4400000000-222-2-222-22-2-22000000000000000000000000000000000000000000000000
χ964-4-444-44-4-2000044-4-42222-2-2-2000000-444-4000000002-2-222-2-222-2-22000000000000000000000000000000000000000000000000
χ974-4-444-44-4-20000-4-4442222-2-2-2000000000000000000−2i32i32i3−2i32i3−2i3−2i32i3-222-2000000000000000000000000000000000000000000000000
χ984-4-444-44-4-20000-4-4442222-2-2-20000000000000000002i3−2i3−2i32i3−2i32i32i3−2i3-222-2000000000000000000000000000000000000000000000000
χ994-4-44-44-4440000000044-4-4-44-40000000000000000000000000000000000000000000000000000000000000000−2i22i22i2−2i20000000000
χ1004-4-44-44-4440000000044-4-4-44-400000000000000000000000000000000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ10188-8-8-8-888-400000000-44-44-444000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-8-88-88-88-400000000-4-4444-44000000000000000000000000000000000000000000000000000000000000000000000000000000

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