Finite Group Databasebeta

← Group #10845940

Character table — Group #10845940

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111112222222222222222222244444444444444444444444444444444444466668888121212121212121212121212121216161616161616161616242424244848
order122222223444466666668888888822446666888812121212121212122424242424242424242424242424242444444444224444888888882466121212121212444424
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
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-1-1-1111111-1-1
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-11-11111-1-1-1-111-1-11-1
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-111-11
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-11111-1-1-1-1-1-111-11
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-11-1-1-1-1111111-1-11-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1-1-11111-11-1-111-1-11111-1-1-11
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-1-1-1-1-111111-111-1-111-1-1-1-1111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1111111-1-1-1-1-11-1-111-1-111-1-1111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1111111-1-1-1-11-111-1-111-1-111-1-1-11
χ17222222222-2-2-2-222222220000000022-2-222220000-2-2-2-2-2-2-2-200000000000000002222000022-2-2-2-2000000000000000000000000
χ18222222222-2-2-2-222222220000000022-2-222220000-2-2-2-2-2-2-2-20000000000000000-2-2-2-20000-2-22222000000000000000000000000
χ19222222222-2-2-2-2222222200000000-2-222-2-2-2-20000-2-2-22222-2000000000000000022220000-2-2-2-222000000000000000000000000
χ20222222222-2-2-2-2222222200000000-2-222-2-2-2-20000-2-2-22222-20000000000000000-2-2-2-200002222-2-2000000000000000000000000
χ2122222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022220000000000000022-1-1-1-1-1-1-1-1000000
χ2222222222-12222-1-1-1-1-1-1-1222222222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-200000000000000-2-211111111000000
χ2322222222-12222-1-1-1-1-1-1-122222222-2-2-2-21111-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-1111111110000222200000000000000-2-211-1-1-1-111000000
χ2422222222-12222-1-1-1-1-1-1-122222222-2-2-2-21111-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-1111111110000-2-2-2-20000000000000022-1-11111-1-1000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-11111111111111111000022-2-2000000000000002-2-1-1-1-11111000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-22222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000-2-22200000000000000-221111-1-1-1-1000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-211112222-1-1-11111-111111111-1-1-1-1-1-1-1-1000022-2-200000000000000-2211-1-111-1-1000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-2-2-2-211112222-1-1-11111-111111111-1-1-1-1-1-1-1-10000-2-222000000000000002-2-1-111-1-111000000
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χ40222-2-2-2-22-12-22-2-111-1-111−2i−2i−2i−2i2i2i2i2i0000i3i3−i3−i30000-1-11i3i3−i3−i31iiii−i−i−i−i3333−3−3−3−30000-222i−2i0000000000000000−i3i31-1−ii−33000000
χ4122-22-2-22-22000022-2-2-22-222−2−222−2−2002i−2i0000−i2−i2i2i20002i−2i2i−2i022−2−222−2−2−i2−i2i2i2−i2−i2i2i222-2-2000000002i−2i22−2−2−i2−i2i2i20000000000000000
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χ4322-22-2-22-22000022-2-2-22-222−2−222−2−200−2i2i0000i2i2−i2−i2000−2i2i−2i2i022−2−222−2−2i2i2−i2−i2i2i2−i2−i222-2-200000000−2i2i22−2−2i2i2−i2−i20000000000000000
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χ4622-22-2-22-22000022-2-2-22-2−2−222−2−222002i−2i0000i2i2−i2−i20002i−2i2i−2i0−2−222−2−222i2i2−i2−i2i2i2−i2−i2-2-22200000000−2i2i22−2−2−i2−i2i2i20000000000000000
χ4722-22-2-22-22000022-2-2-22-2−2−222−2−22200−2i2i0000−i2−i2i2i2000−2i2i−2i2i0−2−222−2−222−i2−i2i2i2−i2−i2i2i222-2-200000000−2i2i−2−222−i2−i2i2i20000000000000000
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χ844-444-44-4-4-200002-2-2-2222−2i22i2−2i22i2−2i22i2−2i22i24-400-22-22−2i22i2−2i22i200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000000000000000000000000000000000
χ854-444-44-4-4-200002-2-2-2222−2i22i2−2i22i2−2i22i2−2i22i2-44002-22-22i2−2i22i2−2i200000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000000000000000000000000000000000
χ864-444-44-4-4-200002-2-2-22222i2−2i22i2−2i22i2−2i22i2−2i24-400-22-222i2−2i22i2−2i200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000000000000000000000000000000000
χ874-444-44-4-4-200002-2-2-22222i2−2i22i2−2i22i2−2i22i2−2i2-44002-22-2−2i22i2−2i22i200000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000000000000000000000000000000000
χ884-44-44-44-440000-4-4-44-44422−2222−22−2222−22220000000000000000000022−2222−22−2222−22220000000000000000000000000000000000000000000000
χ894-44-44-44-440000-4-4-44-444−2222−222222−2222−2200000000000000000000−2222−222222−2222−220000000000000000000000000000000000000000000000
χ904-44-44-44-4-20000222-22-2-222−2222−22−2222−22220000−2i32i32i3−2i3000000000000−22−222−22−2−i6i6−i6i6i6−i6i6−i600000000000000000000000000000000000000
χ914-44-44-44-4-20000222-22-2-222−2222−22−2222−222200002i3−2i3−2i32i3000000000000−22−222−22−2i6−i6i6−i6−i6i6−i6i600000000000000000000000000000000000000
χ924-44-44-44-4-20000222-22-2-2−2222−222222−2222−220000−2i32i32i3−2i30000000000002−22−2−22−22i6−i6i6−i6−i6i6−i6i600000000000000000000000000000000000000
χ934-44-44-44-4-20000222-22-2-2−2222−222222−2222−2200002i3−2i3−2i32i30000000000002−22−2−22−22−i6i6−i6i6i6−i6i6−i600000000000000000000000000000000000000
χ944-4-444-4-44-244-4-42-222-22-24i−4i−4i4i4i−4i−4i4i000000000000-22-200002−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000000000
χ954-4-444-4-44-244-4-42-222-22-2−4i4i4i−4i−4i4i4i−4i000000000000-22-2000022i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000000000
χ964-4-444-4-44-2-4-4442-222-22-200000000000000004-4-442-220000-200000000-222-2-222-200000000000000000000000000000000000000
χ974-4-444-4-44-2-4-4442-222-22-20000000000000000-444-42-220000-2000000002-2-222-2-2200000000000000000000000000000000000000
χ984-4-4-4-44444-444-4-4-44-444-400000000000000000000-4440000-4000000000000000000000000000000000000000000000000000000
χ994-4-4-4-4444-24-4-4422-22-2-224-4-44-444-4000000000000-2220000-2-222-22-2-220000000000000000000000000000000000000000000000
χ1004-4-4-4-4444-24-4-4422-22-2-22-444-44-4-44000000000000-2220000-22-2-22-222-20000000000000000000000000000000000000000000000
χ1014-4-4-4-4444-2-444-422-22-2-22000000000000000000002-2-2000020000000023−23−2323−232323−2300000000000000000000000000000000000000
χ1024-4-4-4-4444-2-444-422-22-2-22000000000000000000002-2-20000200000000−232323−2323−23−232300000000000000000000000000000000000000

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