Finite Group Databasebeta

← Group #10858804

Character table — Group #10858804

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444444444444444444444448888121212121212121216161616161616161616242424242424242424242424
order12222222222234444666666644666688888888121212121212121224242424242424242424242424242424444444444444441212121212121212444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111111111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-111-1-11111-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111-1-1-1-11111
χ911111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11-11111-1-1-1-1-111111-1-1-1-111
χ1011111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-11111111-11111-1-1-1-11-1-1-1-1-11111-1-1
χ1111111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-11-1-1-1-11111-11-1-1-1-111-1-111
χ1211111111-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-11-1-1-1-111111-11111-1-111-1-1
χ1311111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1111-1-111-1-1-1111-1-11111-1-1
χ1411111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1111-1-111-1-11-1-1-111-1-1-1-111
χ1511111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111111111-1-11-1-1-111-1-111-11-1-111-1-111-1-1
χ1611111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1111-1-1-111-1-1111-111-1-111-1-111
χ172222222222222-2-2-2-22222222-2-2222200000000-2-2-2-2-2-2-2-200000000000000000000220000220000000000-2-20000000000
χ182222222222222-2-2-2-22222222-2-2222200000000-2-2-2-2-2-2-2-200000000000000000000-2-20000-2-20000000000220000000000
χ19222222222222-12222-1-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000000022-1-1-1-1-1-1-1-1000000000000
χ20222222222222-12222-1-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-2-211111111000000000000
χ21222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111222200000000-2-2-1-11111-1-1000000000000
χ22222222222222-12222-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2000000002211-1-1-1-111000000000000
χ2322222222-2-2-2-22-2-2-2-2222222222-2-2-2-200000000-2-2-22222-200000000000000000000220000-2-200000000002-20000000000
χ2422222222-2-2-2-22-2-2-2-2222222222-2-2-2-200000000-2-2-22222-200000000000000000000-2-20000220000000000-220000000000
χ2522222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-211112222-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-11111111122-2-2000000002-2-1-1-1-11111000000000000
χ2622222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-211112222-2-2-2-2-1-1-11111-1-1-1-1-1-1-1-1-111111111-2-22200000000-221111-1-1-1-1000000000000
χ2722222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-21111-2-2-2-22222-1-1-11111-111111111-1-1-1-1-1-1-1-122-2-200000000-22-1-111-1-111000000000000
χ2822222222-2-2-2-2-12222-1-1-1-1-1-1-1-2-21111-2-2-2-22222-1-1-11111-111111111-1-1-1-1-1-1-1-1-2-222000000002-211-1-111-1-1000000000000
χ29222-22-2-2-222-2-2222-2-22-2-22-2-222-222-2-20000000022-222-2-2-200000000000000002-22-200000000002-200002-2000000000000
χ30222-22-2-2-222-2-2222-2-22-2-22-2-222-222-2-20000000022-222-2-2-20000000000000000-22-220000000000-220000-22000000000000
χ31222-22-2-2-222-2-22-2-2222-2-22-2-22-2222-2-200000000-2-22-2-222200000000000000000000002i2i−2i−2i000000000000002i−2i00000000
χ32222-22-2-2-222-2-22-2-2222-2-22-2-22-2222-2-200000000-2-22-2-22220000000000000000000000−2i−2i2i2i00000000000000−2i2i00000000
χ33222-22-2-2-222-2-2-122-2-2-111-111-12-2-1-11100000000-1-11-1-11113333−3−3−3−33333−3−3−3−32-22-20000000000-113−33−3-11000000000000
χ34222-22-2-2-222-2-2-122-2-2-111-111-12-2-1-11100000000-1-11-1-11113333−3−3−3−33333−3−3−3−3-22-2200000000001-1−33−331-1000000000000
χ35222-22-2-2-222-2-2-122-2-2-111-111-12-2-1-11100000000-1-11-1-1111−3−3−3−33333−3−3−3−333332-22-20000000000-11−33−33-11000000000000
χ36222-22-2-2-222-2-2-122-2-2-111-111-12-2-1-11100000000-1-11-1-1111−3−3−3−33333−3−3−3−33333-22-2200000000001-13−33−31-1000000000000
χ37222-22-2-2-2-2-222222-2-22-2-22-2-22-22-2-2220000000022-2-2-222-200000000000000002-2-2200000000002-20000-22000000000000
χ38222-22-2-2-2-2-222222-2-22-2-22-2-22-22-2-2220000000022-2-2-222-20000000000000000-222-20000000000-2200002-2000000000000
χ39222-22-2-2-2-2-2222-2-2222-2-22-2-222-2-2-22200000000-2-2222-2-2200000000000000000000002i2i−2i−2i00000000000000−2i2i00000000
χ40222-22-2-2-2-2-2222-2-2222-2-22-2-222-2-2-22200000000-2-2222-2-220000000000000000000000−2i−2i2i2i000000000000002i−2i00000000
χ41222-22-2-2-2-2-222-122-2-2-111-111-1-2211-1-100000000-1-1111-1-113333−3−3−3−3−3−3−3−333332-2-220000000000-113−3−331-1000000000000
χ42222-22-2-2-2-2-222-122-2-2-111-111-1-2211-1-100000000-1-1111-1-113333−3−3−3−3−3−3−3−33333-222-200000000001-1−333−3-11000000000000
χ43222-22-2-2-2-2-222-122-2-2-111-111-1-2211-1-100000000-1-1111-1-11−3−3−3−333333333−3−3−3−32-2-220000000000-11−333−31-1000000000000
χ44222-22-2-2-2-2-222-122-2-2-111-111-1-2211-1-100000000-1-1111-1-11−3−3−3−333333333−3−3−3−3-222-200000000001-13−3−33-11000000000000
χ4522-2-2-22-222-22-2200002-2-2-222-2002-22-2−i2−i2i2i2−i2−i2i2i200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200002-200002-2000000000000000000−i2i2−i2i2
χ4622-2-2-22-222-22-2200002-2-2-222-2002-22-2−i2−i2i2i2−i2−i2i2i200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000-220000-22000000000000000000i2−i2i2−i2
χ4722-2-2-22-222-22-2200002-2-2-222-2002-22-2i2i2−i2−i2i2i2−i2−i200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200002-200002-2000000000000000000i2−i2i2−i2
χ4822-2-2-22-222-22-2200002-2-2-222-2002-22-2i2i2−i2−i2i2i2−i2−i200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000-220000-22000000000000000000−i2i2−i2i2
χ4922-2-2-22-22-22-22200002-2-2-222-200-22-22−i2−i2i2i2i2i2−i2−i200000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200002-20000-22000000000000000000i2−i2−i2i2
χ5022-2-2-22-22-22-22200002-2-2-222-200-22-22−i2−i2i2i2i2i2−i2−i200000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000-2200002-2000000000000000000−i2i2i2−i2
χ5122-2-2-22-22-22-22200002-2-2-222-200-22-22i2i2−i2−i2−i2−i2i2i200000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200002-20000-22000000000000000000−i2i2i2−i2
χ5222-2-2-22-22-22-22200002-2-2-222-200-22-22i2i2−i2−i2−i2−i2i2i200000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000-2200002-2000000000000000000i2−i2−i2i2
χ532-2-222-2-22000022-22-2-22-2-22-2200000000002i−2i2i−2i2-220000-2000000002i−2i2i−2i2i−2i2i−2i0000002i−2i2i−2i00000000000000002-2000000
χ542-2-222-2-22000022-22-2-22-2-22-2200000000002i−2i2i−2i2-220000-2000000002i−2i2i−2i2i−2i2i−2i000000−2i2i−2i2i0000000000000000-22000000
χ552-2-222-2-22000022-22-2-22-2-22-220000000000−2i2i−2i2i2-220000-200000000−2i2i−2i2i−2i2i−2i2i0000002i−2i2i−2i0000000000000000-22000000
χ562-2-222-2-22000022-22-2-22-2-22-220000000000−2i2i−2i2i2-220000-200000000−2i2i−2i2i−2i2i−2i2i000000−2i2i−2i2i00000000000000002-2000000
χ572-2-2-2222-200002-222-2-2-22-2-2220000002i−2i2i−2i0000-2220000-22i−2i2i−2i2i−2i2i−2i000000000000002-2-220000000000000000002i−2i0000
χ582-2-2-2222-200002-222-2-2-22-2-2220000002i−2i2i−2i0000-2220000-22i−2i2i−2i2i−2i2i−2i00000000000000-222-2000000000000000000−2i2i0000
χ592-2-2-2222-200002-222-2-2-22-2-222000000−2i2i−2i2i0000-2220000-2−2i2i−2i2i−2i2i−2i2i000000000000002-2-22000000000000000000−2i2i0000
χ602-2-2-2222-200002-222-2-2-22-2-222000000−2i2i−2i2i0000-2220000-2−2i2i−2i2i−2i2i−2i2i00000000000000-222-20000000000000000002i−2i0000
χ61444444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4-2-2-2-2000000002222222200000000000000000000000000000000000000000000000000
χ6244444444-4-4-4-4-2-4-4-4-4-2-2-2-2-2-2-244222200000000222-2-2-2-2200000000000000000000000000000000000000000000000000
χ63444-44-4-4-444-4-4-2-4-444-222-222-2-44-2-2220000000022-222-2-2-200000000000000000000000000000000000000000000000000
χ64444-44-4-4-4-4-444-2-4-444-222-222-24-422-2-20000000022-2-2-222-200000000000000000000000000000000000000000000000000
χ6544-44-4-44-44-4-4440000444-4-4-4-4004-4-44000000000000000000000000000000000000000000000000000000000000000000
χ6644-44-4-44-44-4-44-20000-2-2-2222200-222-20000000000000000i6i6−i6−i6−i6−i6i6i6i6i6−i6−i6−i6−i6i6i60000000000000000000000000000000000
χ6744-44-4-44-44-4-44-20000-2-2-2222200-222-20000000000000000−i6−i6i6i6i6i6−i6−i6−i6−i6i6i6i6i6−i6−i60000000000000000000000000000000000
χ6844-44-4-44-4-444-440000444-4-4-4-400-444-4000000000000000000000000000000000000000000000000000000000000000000
χ6944-44-4-44-4-444-4-20000-2-2-22222002-2-220000000000000000i6i6−i6−i6−i6−i6i6i6−i6−i6i6i6i6i6−i6−i60000000000000000000000000000000000
χ7044-44-4-44-4-444-4-20000-2-2-22222002-2-220000000000000000−i6−i6i6i6i6i6−i6−i6i6i6−i6−i6−i6−i6i6i60000000000000000000000000000000000
χ7144-4-4-44-444-44-4-20000-2222-2-2200-22-22−2i2−2i22i22i2−2i2−2i22i22i200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000000000000000000000
χ7244-4-4-44-444-44-4-20000-2222-2-2200-22-222i22i2−2i2−2i22i22i2−2i2−2i200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000000000000000000000
χ7344-4-4-44-44-44-44-20000-2222-2-22002-22-2−2i2−2i22i22i22i22i2−2i2−2i200000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i20000000000000000000000000000000000
χ7444-4-4-44-44-44-44-20000-2222-2-22002-22-22i22i2−2i2−2i2−2i2−2i22i22i200000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i20000000000000000000000000000000000
χ754-444-44-4-4000040000-44-44-44-400000022−22−222200000000000022−22−222222−22−2222000000000000000000000000000000000000000000
χ764-444-44-4-4000040000-44-44-44-4000000−222222−22000000000000−222222−22−222222−22000000000000000000000000000000000000000000
χ774-444-44-4-40000-200002-22-22-2200000022−22−2222000000023−2323−230−222−2−222−26−6−66−666−60000000000000000000000000000000000
χ784-444-44-4-40000-200002-22-22-2200000022−22−22220000000−2323−23230−222−2−222−2−666−66−6−660000000000000000000000000000000000
χ794-444-44-4-40000-200002-22-22-22000000−222222−22000000023−2323−2302−2−222−2−22−666−66−6−660000000000000000000000000000000000
χ804-444-44-4-40000-200002-22-22-22000000−222222−220000000−2323−232302−2−222−2−226−6−66−666−60000000000000000000000000000000000
χ814-44-4-4-444000040000-4-4444-4-4000000000022−22−2222000000000000000022−22−222222−22−22220000000000000000000000000000000000
χ824-44-4-4-444000040000-4-4444-4-40000000000−222222−220000000000000000−222222−22−222222−220000000000000000000000000000000000
χ834-44-4-4-4440000-2000022-2-2-222000000000022−22−222200023−23−23230−666−66−6−66−222−2−222−20000000000000000000000000000000000
χ844-44-4-4-4440000-2000022-2-2-222000000000022−22−2222000−232323−2306−6−66−666−6−222−2−222−20000000000000000000000000000000000
χ854-44-4-4-4440000-2000022-2-2-2220000000000−222222−2200023−23−232306−6−66−666−62−2−222−2−220000000000000000000000000000000000
χ864-44-4-4-4440000-2000022-2-2-2220000000000−222222−22000−232323−230−666−66−6−662−2−222−2−220000000000000000000000000000000000
χ874-4-444-4-4400004-44-44-44-4-44-4400000000000000-44-40000400000000000000000000000000000000000000000000000000
χ884-4-444-4-440000-24-44-42-222-22-200000000004i−4i4i−4i-22-20000200000000−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000
χ894-4-444-4-440000-24-44-42-222-22-20000000000−4i4i−4i4i-22-200002000000002i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000
χ904-4-444-4-440000-2-44-442-222-22-2000000000000002-220000-2−2i32i3−2i32i32i3−2i32i3−2i3000000000000000000000000000000000000000000
χ914-4-444-4-440000-2-44-442-222-22-2000000000000002-220000-22i3−2i32i3−2i3−2i32i3−2i32i3000000000000000000000000000000000000000000
χ924-4-4-4444-4000044-4-44-4-44-4-444000000000000004-4-40000400000000000000000000000000000000000000000000000000
χ934-4-4-4444-40000-24-4-4422-222-2-200000000000000-2220000-200000000−2i32i3−2i32i32i3−2i32i3−2i30000000000000000000000000000000000
χ944-4-4-4444-40000-24-4-4422-222-2-200000000000000-2220000-2000000002i3−2i32i3−2i3−2i32i3−2i32i30000000000000000000000000000000000
χ954-4-4-4444-40000-2-444-422-222-2-20000004i−4i4i−4i00002-2-200002−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000
χ964-4-4-4444-40000-2-444-422-222-2-2000000−4i4i−4i4i00002-2-2000022i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000

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