Finite Group Databasebeta

← Group #10848727

Character table — Group #10848727

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222244444444444444444444444444444444444466668888121212121212121212121212121216161616161616161616242424244848
order122222223444444444444666666688888888121212121212121212121212242424242424242424242424242424244444444422444488888888441212121212121212224424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1
χ9111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-11-111-1-111-1-111-1-11-1
χ10111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1-11-1-111-1-111-1-111-11
χ11111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111111-111-1-111-1-1-1-111-11
χ12111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-11-1-111-1-11111-1-11-1
χ13111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-11111-11-1-11111-1-111-1-1-11
χ14111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-111111-111-1-1-1-111-1-1111-1
χ15111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1111111-1-1-1-1-11-1-11111-1-1-1-1111-1
χ16111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1111111-1-1-1-11-111-1-1-1-11111-1-1-11
χ172222222222222-2-2-2-2-2-2-2-2222222200000000-2-22222-2-2-2-2-2-200000000000000002222000022-2-2-2-2000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-2222222200000000-2-22222-2-2-2-2-2-20000000000000000-2-2-2-20000-2-22222000000000000000000000000
χ19222222222-2-2-2-22222-2-2-2-2222222200000000-2-2-2-2-2-22222-2-2000000000000000022220000-2-2-2-222000000000000000000000000
χ20222222222-2-2-2-22222-2-2-2-2222222200000000-2-2-2-2-2-22222-2-20000000000000000-2-2-2-200002222-2-2000000000000000000000000
χ2122222222-1222222222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022220000000000000022-1-1-1-1-1-1-1-1000000
χ2222222222-1222222222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-200000000000000-2-211111111000000
χ2322222222-1222222222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000222200000000000000-2-21111-1-1-1-1000000
χ2422222222-1222222222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000-2-2-2-20000000000000022-1-1-1-11111000000
χ2522222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-111111111000022-2-2000000000000002-2-1-111-1-111000000
χ2622222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-12222-2-2-2-2-1-111111111-1-1-1-1-1-1-1-1-1-1111111110000-2-22200000000000000-2211-1-111-1-1000000
χ2722222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-1000022-2-200000000000000-2211-1-1-1-111000000
χ2822222222-1-2-2-2-2-2-2-2-22222-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-111111111-1-1-1-1-1-1-1-10000-2-222000000000000002-2-1-11111-1-1000000
χ29222-2-2-2-222000000002-22-2222-2-2-2-2000022-2-22-2000000002-2000000002222-2-2-2-22i2i−2i−2i0000002i−2i0000002i2i−2i−2i0000000000000000
χ30222-2-2-2-222000000002-22-2222-2-2-2-2000022-2-22-2000000002-2000000002222-2-2-2-2−2i−2i2i2i000000−2i2i000000−2i−2i2i2i0000000000000000
χ31222-2-2-2-222000000002-22-2222-2-2-2-20000-2-2222-2000000002-200000000-2-2-2-222222i2i−2i−2i0000002i−2i000000−2i−2i2i2i0000000000000000
χ32222-2-2-2-222000000002-22-2222-2-2-2-20000-2-2222-2000000002-200000000-2-2-2-22222−2i−2i2i2i000000−2i2i0000002i2i−2i−2i0000000000000000
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χ36222-2-2-2-22200000000-22-22222-2-2-2-2-2-2220000-2200000000-22-2-2-2-2222200000000−2i−2i2i2i0000002i−2i002i2i−2i−2i00000000000000000000
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χ3822-22-22-2-2200002i2i−2i−2i00002-2-22-22-22−22−2−i2i2−i2i20000002i2i−2i−2i0022−2−222−2−2−i2−i2i2i2−i2−i2i2i2-22-2200000000−2i2i−22−22i2−i2i2−i20000000000000000
χ3922-22-22-2-2200002i2i−2i−2i00002-2-22-22-2−22−22i2−i2i2−i20000002i2i−2i−2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i22-22-2000000002i−2i−22−22i2−i2i2−i20000000000000000
χ4022-22-22-2-2200002i2i−2i−2i00002-2-22-22-2−22−22i2−i2i2−i20000002i2i−2i−2i00−2−222−2−222i2i2−i2−i2i2i2−i2−i2-22-2200000000−2i2i2−22−2−i2i2−i2i20000000000000000
χ4122-22-22-2-220000−2i−2i2i2i00002-2-22-22-22−22−2i2−i2i2−i2000000−2i−2i2i2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i22-22-200000000−2i2i2−22−2i2−i2i2−i20000000000000000
χ4222-22-22-2-220000−2i−2i2i2i00002-2-22-22-22−22−2i2−i2i2−i2000000−2i−2i2i2i0022−2−222−2−2i2i2−i2−i2i2i2−i2−i2-22-22000000002i−2i−22−22−i2i2−i2i20000000000000000
χ4322-22-22-2-220000−2i−2i2i2i00002-2-22-22-2−22−22−i2i2−i2i2000000−2i−2i2i2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i22-22-200000000−2i2i−22−22−i2i2−i2i20000000000000000
χ4422-22-22-2-220000−2i−2i2i2i00002-2-22-22-2−22−22−i2i2−i2i2000000−2i−2i2i2i00−2−222−2−222−i2−i2i2i2−i2−i2i2i2-22-22000000002i−2i2−22−2i2−i2i2−i20000000000000000
χ4522-2-22-22-222i2i−2i−2i000000002-2-2-22-222−2−22−i2i2i2−i2002i2i−2i−2i00000022−2−2−2−222−i2−i2i2i2i2i2−i2−i22i−2i−2i2i00002-20000i2−i2−i2i22−2−220000000000000000
χ4622-2-22-22-222i2i−2i−2i000000002-2-2-22-222−2−22−i2i2i2−i2002i2i−2i−2i00000022−2−2−2−222−i2−i2i2i2i2i2−i2−i2−2i2i2i−2i0000-220000−i2i2i2−i2−222−20000000000000000
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χ532-2-2-2-222222-22-22-22-222-2-2-2-22-2-22200000000-2-22-22-22-22-2220000000000000000000000000000000000000000000000002-22-200
χ542-2-2-2-222222-22-22-22-222-2-2-2-22-2-22200000000-2-22-22-22-22-222000000000000000000000000000000000000000000000000-22-2200
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χ934-44-444-4-4-20000−4i4i4i−4i00002-222-2-22000000000000002i−2i−2i2i006−6−666−6−66−i6i6i6−i6−i6i6i6−i600000000000000000000000000000000000000
χ944-44-444-4-4-20000−4i4i4i−4i00002-222-2-22000000000000002i−2i−2i2i00−666−6−666−6i6−i6−i6i6i6−i6−i6i600000000000000000000000000000000000000
χ954-4-444-4-444000000004-4-44-4-4444-4-400000000-44000000004-4000000000000000000000000000000000000000000000000000000
χ964-4-444-4-44400000000-444-4-4-4444-4-4000000004-400000000-44000000000000000000000000000000000000000000000000000000
χ974-4-444-4-44-2000000004-4-4422-2-2-222000000002-200000000-2223−2323−23−2323−23230000000000000000000000000000000000000000000000
χ984-4-444-4-44-2000000004-4-4422-2-2-222000000002-200000000-22−2323−232323−2323−230000000000000000000000000000000000000000000000
χ994-4-444-4-44-200000000-444-422-2-2-22200000000-22000000002-20000000023−2323−23−2323−232300000000000000000000000000000000000000
χ1004-4-444-4-44-200000000-444-422-2-2-22200000000-22000000002-200000000−2323−232323−2323−2300000000000000000000000000000000000000
χ1014-4-4-4-4444-24-44-44-44-444-4-422-222-2-20000000022-22-22-22-22-2-2000000000000000000000000000000000000000000000000000000
χ1024-4-4-4-4444-2-44-44-44-4444-4-422-222-2-200000000222-22-22-22-2-2-2000000000000000000000000000000000000000000000000000000

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