Finite Group Databasebeta

← Group #10853319

Character table — Group #10853319

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222444444444444444444444444444444444488888888888888888888888888121212121212121224242424242424244848
order12222222344444444666666644444444441212121212121212121212121212121212121212121212122244444466661212121212121212121212121212888888884444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1
χ911111111111-1-1-1-1111111111-1-1111111-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-11-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-11-1
χ1011111111111-1-1-1-1111111111-1-1111111-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-11-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-11
χ1111111111111-1-1-1-1111111111-1-11111-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-111-11-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-111-11
χ1211111111111-1-1-1-1111111111-1-11111-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-111-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-11-1
χ1311111111111-1-1-1-1111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-11111-1-111-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-11
χ1411111111111-1-1-1-1111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111-1
χ1511111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-1111-1
χ1611111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-11
χ17222222222-2-22222-2-22222222-2-200002222-2-2-2-222222222222200000000000000-2-20000-2-2-2-2-2-200000000000000000000000000
χ18222222222-2-22222-2-22222222-2-20000-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000220000-2-2222200000000000000000000000000
χ19222222222-2-2-2-2-2-2-2-2222222222000022-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000000000-22000022-2-22200000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-22222222220000-2-222-2-2-2-2-2-2-2-22222-2-2-2-2000000000000002-200002222-2-200000000000000000000000000
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
χ2222222222-122222222-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-1-1-1-1-1-1111111111111000000000000000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-2-2-2-2-2-2221111-1-1-1-1-1-111111111000000000000000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-111111111-1-1-1-111111111-2-22222-2-21111-1-11111-1-1-1-1-1-1-1-1000000000000000000
χ2522222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2222222-2-2-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-2-222-2-22-2111111-1-111-1-1-1-11111000000000000000000
χ2622222222-122-2-2-2-222-1-1-1-1-1-1-1-2-22222-2-222-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-2-2-2-222-2211111111-1-11111-1-1-1-1000000000000000000
χ2722222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-2-2-222-2-2-1-1-1-1-1-1-1-1111111111111111122-2-2222-2-1-1-1-111-1-1111111-1-1-1-1000000000000000000
χ2822222222-122-2-2-2-222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-1-1-1-11111-1-1-1-11111111111112222-2-2-22-1-1-1-11111-1-1-1-1-1-11111000000000000000000
χ2922222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-2000022221111-1-1-1-1-1-1-1-1-1-1-1-1−i3−i3−i3−i3i3i3i3i3000000-2-2−i3−i3i3i3111111−i3−i3i3i3−i3−i3i3i3000000000000000000
χ3022222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-2000022221111-1-1-1-1-1-1-1-1-1-1-1-1i3i3i3i3−i3−i3−i3−i3000000-2-2i3i3−i3−i3111111i3i3−i3−i3i3i3−i3−i3000000000000000000
χ3122222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-20000-2-2-2-2111111111111-1-1-1-1−i3−i3−i3−i3i3i3i3i300000022−i3−i3i3i311-1-1-1-1i3i3−i3−i3i3i3−i3−i3000000000000000000
χ3222222222-1-2-22222-2-2-1-1-1-1-1-1-1-2-20000-2-2-2-2111111111111-1-1-1-1i3i3i3i3−i3−i3−i3−i300000022i3i3−i3−i311-1-1-1-1−i3−i3i3i3−i3−i3i3i3000000000000000000
χ3322222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122000022-2-21111-1-1-1-111111111−i3−i3−i3−i3i3i3i3i3000000-22i3i3−i3−i3-1-111-1-1−i3−i3i3i3i3i3−i3−i3000000000000000000
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χ3522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000-2-22211111111-1-1-1-11111−i3−i3−i3−i3i3i3i3i30000002-2i3i3−i3−i3-1-1-1-111i3i3−i3−i3−i3−i3i3i3000000000000000000
χ3622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000-2-22211111111-1-1-1-11111i3i3i3i3−i3−i3−i3−i30000002-2−i3−i3i3i3-1-1-1-111−i3−i3i3i3i3i3−i3−i3000000000000000000
χ37222-2-2-22-222-20000-2222-2-2-2-22002i2i−2i−2i000022-2-20000000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000002i2i−2i−2i0000002-2000000
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χ40222-2-2-22-222-20000-2222-2-2-2-2200−2i−2i2i2i000022-2-2000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000000000−2i−2i2i2i0000002-2000000
χ4122-2-22-2-2220022-2-2002-2-22-22-20000002i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i22-2-20000000000000000000000000000000000−i2i2−i2i2−i2−i2i2i200002−22−200
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χ492-2222-2-2-22222-22-2-2-2-222-2-22-22-22-22-200002-22-2000000002-22-22-22-22-22-22-20000002-22-22-2000000000000000000000000000000
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χ522-2222-2-2-2222-22-22-2-2-222-2-22-2-22-22-2200002-22-200000000-22-22-22-22-22-222-20000002-22-2-22000000000000000000000000000000
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χ552-2222-2-2-22-2-2-22-2222-222-2-22-22-200000000-22-2200000000-22-2200000000002i−2i−2i2i0000002-200002i−2i2i−2i−2i2i−2i2i000000000000000000
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χ572-2222-2-2-2-1222-22-2-2-21-1-111-112-22-22-20000-11-113−33−33−33−3-11-11-11-11-11-112-2000000-11-11-113−33−33−3−333−3−33000000000000000000
χ582-2222-2-2-2-1222-22-2-2-21-1-111-112-22-22-20000-11-11−33−33−33−33-11-11-11-11-11-112-2000000-11-11-11−33−33−333−3−333−3000000000000000000
χ592-2222-2-2-2-1222-22-2-2-21-1-111-112-2-22-220000-11-113−33−33−33−3-11-111-11-11-11-1-220000001-11-1-113−33−3−333−3−333−3000000000000000000
χ602-2222-2-2-2-1222-22-2-2-21-1-111-112-2-22-220000-11-11−33−33−33−33-11-111-11-11-11-1-220000001-11-1-11−33−333−3−333−3−33000000000000000000
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χ622-2222-2-2-2-122-22-22-2-21-1-111-11-222-22-20000-11-11−33−333−33−31-11-1-11-11-11-11-220000001-11-11-1−333−3−333−33−3−33000000000000000000
χ632-2222-2-2-2-122-22-22-2-21-1-111-11-22-22-220000-11-113−33−3−33−331-11-11-11-11-11-12-2000000-11-111-13−3−33−333−33−3−33000000000000000000
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χ914-44-4-44-44-2-440000-442-22-2-22200000000002-2-2200000000000023−23−2323−232323−2300000000000000000000000000000000000000000000
χ924-44-4-44-44-2-440000-442-22-2-22200000000002-2-22000000000000−232323−2323−23−232300000000000000000000000000000000000000000000
χ934-4-44-4-444400000000-4-444-4-44000000000000000000000000000000000000000000000000000000000000000022−22−22220000000000
χ944-4-44-4-444400000000-4-444-4-440000000000000000000000000000000000000000000000000000000000000000−222222−220000000000
χ954-4-4-4444-44004-4-4400-4-4-4-444400000000000000000000004-4-440000000000000000000000000000000000000000000000000000
χ964-4-4-4444-4400-444-400-4-4-4-44440000000000000000000000-444-40000000000000000000000000000000000000000000000000000
χ974-4-4-4444-4-2004-4-44002222-2-2-200000000000000−2i32i32i3−2i3−2i32i32i3−2i3-222-20000000000000000000000000000000000000000000000000000
χ984-4-4-4444-4-2004-4-44002222-2-2-2000000000000002i3−2i3−2i32i32i3−2i3−2i32i3-222-20000000000000000000000000000000000000000000000000000
χ994-4-4-4444-4-200-444-4002222-2-2-200000000000000−2i32i32i3−2i32i3−2i3−2i32i32-2-220000000000000000000000000000000000000000000000000000
χ1004-4-4-4444-4-200-444-4002222-2-2-2000000000000002i3−2i3−2i32i3−2i32i32i3−2i32-2-220000000000000000000000000000000000000000000000000000
χ10188-88-88-8-8-400000000-44-44-444000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-8-88-8-888-40000000044-4-444-4000000000000000000000000000000000000000000000000000000000000000000000000000000

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