Finite Group Databasebeta

← Group #351663

Character table — Group #351663

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11111111222222222222222222222222222222224444444444444444444444444444444444444444444444161616161616161632323232
order12222222444444444444444488888888888888884444444444444444444444888888888888888888888888888888882444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111-1-1
χ911111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ1011111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ1111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-11
χ1211111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ1311111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-11
χ1411111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-111-1
χ1511111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-111-111-1
χ1611111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-11-1-11
χ172222222222222222-2-22222-2-22222222222222222-2-2-2-200000000-2-200000000-2-2-2-2-2-2-2-20000000000000000000000000000
χ182222222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000-2-200000000222222220000000000000000000000000000
χ19222222222222-2-2-2-222-2-2-2-222000000000000000022-2-22222-2-2-2-2-2-22222-2-2-2-2000000000000000000000000000000000000
χ20222222222222-2-2-2-222-2-2-2-222000000000000000022-2-2-2-2-2-22222-2-2-2-2-2-22222000000000000000000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-222000000002200000000000000002i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i000000000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-22200000000220000000000000000−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i000000000000
χ2322222222-2-2-2-2222222-2-2-2-2220000000000000000-2-2222222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000
χ2422222222-2-2-2-2222222-2-2-2-2220000000000000000-2-222-2-2-2-22222-2-22222-2-2-2-2000000000000000000000000000000000000
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000022-2-2000000002200000000000000002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i000000000000
χ2622222222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000022-2-200000000220000000000000000−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-222222222-2-2-2-2-2-2-2-2222200000000-2-200000000-2-2-2-222220000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-222222222222200000000-2-2000000002222-2-2-2-20000000000000000000000000000
χ29222-2-22-2-222-2-222-2-200-2-222002i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000000000i2−i2i2−i22−22−20000
χ30222-2-22-2-222-2-222-2-200-2-222002i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000000000−i2i2−i2i2−22−220000
χ31222-2-22-2-222-2-222-2-200-2-22200−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000000000i2−i2i2−i2−22−220000
χ32222-2-22-2-222-2-222-2-200-2-22200−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000000000−i2i2−i2i22−22−20000
χ33222-2-22-2-2-2-222-2-22200-2-222002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000000000i2−i2−i2i22−2−220000
χ34222-2-22-2-2-2-222-2-22200-2-222002i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000000000−i2i2i2−i2−222−20000
χ35222-2-22-2-2-2-222-2-22200-2-22200−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000000000i2−i2−i2i2−222−20000
χ36222-2-22-2-2-2-222-2-22200-2-22200−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000000000−i2i2i2−i22−2−220000
χ3722-22-2-22-200002i−2i2i−2i2-200002-2i2i2−i2−i2i2i2−i2−i222−2−222−2−2002i−2i00002i2i−2i−2i0022-2-20000i2i2−i2−i222−2−222−2−222−2−2i2i2−i2−i2i2i2−i2−i2000000000000
χ3822-22-2-22-200002i−2i2i−2i2-200002-2i2i2−i2−i2i2i2−i2−i222−2−222−2−2002i−2i0000−2i−2i2i2i00-2-2220000i2i2−i2−i222−2−2−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000000000
χ3922-22-2-22-200002i−2i2i−2i2-200002-2−i2−i2i2i2−i2−i2i2i2−2−222−2−222002i−2i00002i2i−2i−2i0022-2-20000−i2−i2i2i2−2−222−2−222−2−222−i2−i2i2i2−i2−i2i2i2000000000000
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χ4122-22-2-22-200002i−2i2i−2i-220000-22i2i2−i2−i2i2i2−i2−i222−2−222−2−200−2i2i22-2-200000000002i2i−2i−2i−i2−i2i2i2−2−222i2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000
χ4222-22-2-22-200002i−2i2i−2i-220000-22i2i2−i2−i2i2i2−i2−i222−2−222−2−200−2i2i-2-2220000000000−2i−2i2i2i−i2−i2i2i2−2−222−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000
χ4322-22-2-22-200002i−2i2i−2i-220000-22−i2−i2i2i2−i2−i2i2i2−2−222−2−22200−2i2i22-2-200000000002i2i−2i−2ii2i2−i2−i222−2−2−i2−i2i2i2i2i2−i2−i2−2−22222−2−2000000000000
χ4422-22-2-22-200002i−2i2i−2i-220000-22−i2−i2i2i2−i2−i2i2i2−2−222−2−22200−2i2i-2-2220000000000−2i−2i2i2ii2i2−i2−i222−2−2i2i2−i2−i2−i2−i2i2i222−2−2−2−222000000000000
χ4522-22-2-22-20000−2i2i−2i2i2-200002-2i2i2−i2−i2i2i2−i2−i2−2−222−2−22200−2i2i00002i2i−2i−2i00-2-2220000i2i2−i2−i2−2−22222−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000000000
χ4622-22-2-22-20000−2i2i−2i2i2-200002-2i2i2−i2−i2i2i2−i2−i2−2−222−2−22200−2i2i0000−2i−2i2i2i0022-2-20000i2i2−i2−i2−2−222−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000000000
χ4722-22-2-22-20000−2i2i−2i2i2-200002-2−i2−i2i2i2−i2−i2i2i222−2−222−2−200−2i2i00002i2i−2i−2i00-2-2220000−i2−i2i2i222−2−2−2−222−2−222i2i2−i2−i2i2i2−i2−i2000000000000
χ4822-22-2-22-20000−2i2i−2i2i2-200002-2−i2−i2i2i2−i2−i2i2i222−2−222−2−200−2i2i0000−2i−2i2i2i0022-2-20000−i2−i2i2i222−2−222−2−222−2−2−i2−i2i2i2−i2−i2i2i2000000000000
χ4922-22-2-22-20000−2i2i−2i2i-220000-22i2i2−i2−i2i2i2−i2−i2−2−222−2−222002i−2i22-2-20000000000−2i−2i2i2i−i2−i2i2i222−2−2i2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000
χ5022-22-2-22-20000−2i2i−2i2i-220000-22i2i2−i2−i2i2i2−i2−i2−2−222−2−222002i−2i-2-22200000000002i2i−2i−2i−i2−i2i2i222−2−2−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000
χ5122-22-2-22-20000−2i2i−2i2i-220000-22−i2−i2i2i2−i2−i2i2i222−2−222−2−2002i−2i22-2-20000000000−2i−2i2i2ii2i2−i2−i2−2−222−i2−i2i2i2i2i2−i2−i222−2−2−2−222000000000000
χ5222-22-2-22-20000−2i2i−2i2i-220000-22−i2−i2i2i2−i2−i2i2i222−2−222−2−2002i−2i-2-22200000000002i2i−2i−2ii2i2−i2−i2−2−222i2i2−i2−i2−i2−i2i2i2−2−22222−2−2000000000000
χ532-22-22-22-22i−2i2i−2i00002-20000-22i2−i2i2−i2i2−i2i2−i22−22−22−22−22i−2i0000002-22-20000002i−2i2i−2ii2−i2i2−i22−22−2i2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000
χ542-22-22-22-22i−2i2i−2i00002-20000-22i2−i2i2−i2i2−i2i2−i22−22−22−22−22i−2i000000-22-22000000−2i2i−2i2ii2−i2i2−i22−22−2−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000
χ552-22-22-22-22i−2i2i−2i00002-20000-22−i2i2−i2i2−i2i2−i2i2−22−22−22−222i−2i0000002-22-20000002i−2i2i−2i−i2i2−i2i2−22−22−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000
χ562-22-22-22-22i−2i2i−2i00002-20000-22−i2i2−i2i2−i2i2−i2i2−22−22−22−222i−2i000000-22-22000000−2i2i−2i2i−i2i2−i2i2−22−22i2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000
χ572-22-22-22-22i−2i2i−2i0000-2200002-2i2−i2i2−i2i2−i2i2−i22−22−22−22−2−2i2i002i−2i2i−2i0000002-22-20000−i2i2−i2i2−22−222−22−2−22−22−i2i2−i2i2i2−i2i2−i2000000000000
χ582-22-22-22-22i−2i2i−2i0000-2200002-2i2−i2i2−i2i2−i2i2−i22−22−22−22−2−2i2i00−2i2i−2i2i000000-22-220000−i2i2−i2i2−22−22−22−222−22−2i2−i2i2−i2−i2i2−i2i2000000000000
χ592-22-22-22-22i−2i2i−2i0000-2200002-2−i2i2−i2i2−i2i2−i2i2−22−22−22−22−2i2i002i−2i2i−2i0000002-22-20000i2−i2i2−i22−22−2−22−222−22−2i2−i2i2−i2−i2i2−i2i2000000000000
χ602-22-22-22-22i−2i2i−2i0000-2200002-2−i2i2−i2i2−i2i2−i2i2−22−22−22−22−2i2i00−2i2i−2i2i000000-22-220000i2−i2i2−i22−22−22−22−2−22−22−i2i2−i2i2i2−i2i2−i2000000000000
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χ632-22-22-22-2−2i2i−2i2i00002-20000-22−i2i2−i2i2−i2i2−i2i22−22−22−22−2−2i2i0000002-22-2000000−2i2i−2i2i−i2i2−i2i22−22−2−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000000000
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χ652-22-22-22-2−2i2i−2i2i0000-2200002-2i2−i2i2−i2i2−i2i2−i2−22−22−22−222i−2i002i−2i2i−2i000000-22-220000−i2i2−i2i22−22−22−22−2−22−22i2−i2i2−i2−i2i2−i2i2000000000000
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χ672-22-22-22-2−2i2i−2i2i0000-2200002-2−i2i2−i2i2−i2i2−i2i22−22−22−22−22i−2i002i−2i2i−2i000000-22-220000i2−i2i2−i2−22−22−22−222−22−2−i2i2−i2i2i2−i2i2−i2000000000000
χ682-22-22-22-2−2i2i−2i2i0000-2200002-2−i2i2−i2i2−i2i2−i2i22−22−22−22−22i−2i00−2i2i−2i2i0000002-22-20000i2−i2i2−i2−22−222−22−2−22−22i2−i2i2−i2−i2i2−i2i2000000000000
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χ702-2-2-2-222200000000222-22-2-2-2000000002-2-222-2-220000−2i2i2i−2i2i−2i−2i2i2-20000000000002-2-22000000002i−2i−2i2i2i−2i−2i2i000000000000
χ712-2-2-2-222200000000222-22-2-2-200000000-222-2-222-200002i−2i−2i2i−2i2i2i−2i2-2000000000000-222-2000000002i−2i−2i2i2i−2i−2i2i000000000000
χ722-2-2-2-222200000000222-22-2-2-200000000-222-2-222-20000−2i2i2i−2i2i−2i−2i2i2-2000000000000-222-200000000−2i2i2i−2i−2i2i2i−2i000000000000
χ732-2-2-2-22220000000022-22-22-2-22-2-222-2-220000000000002i−2i−2i2i2i−2i−2i2i-22000000002-2-220000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ742-2-2-2-22220000000022-22-22-2-22-2-222-2-22000000000000−2i2i2i−2i−2i2i2i−2i-22000000002-2-2200002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ752-2-2-2-22220000000022-22-22-2-2-222-2-222-20000000000002i−2i−2i2i2i−2i−2i2i-2200000000-222-200002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ762-2-2-2-22220000000022-22-22-2-2-222-2-222-2000000000000−2i2i2i−2i−2i2i2i−2i-2200000000-222-20000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ772-2-2-2-222200000000-2-22-22-222000000002-2-222-2-22000000000000-222-2-222-2-220000-222-22-2-22-222-200000000000000000000
χ782-2-2-2-222200000000-2-22-22-222000000002-2-222-2-22000000000000-22-222-2-222-20000-222-2-222-22-2-2200000000000000000000
χ792-2-2-2-222200000000-2-22-22-22200000000-222-2-222-2000000000000-222-2-222-2-2200002-2-22-222-22-2-2200000000000000000000
χ802-2-2-2-222200000000-2-22-22-22200000000-222-2-222-2000000000000-22-222-2-222-200002-2-222-2-22-222-200000000000000000000
χ812-2-2-2-222200000000-2-2-22-22222-2-222-2-22000000000000000000002-22-2-22-222-2-222-2000000000000-222-22-2-22000000000000
χ822-2-2-2-222200000000-2-2-22-22222-2-222-2-22000000000000000000002-2-222-22-2-22-222-20000000000002-2-22-222-2000000000000
χ832-2-2-2-222200000000-2-2-22-2222-222-2-222-2000000000000000000002-22-2-22-222-22-2-220000000000002-2-22-222-2000000000000
χ842-2-2-2-222200000000-2-2-22-2222-222-2-222-2000000000000000000002-2-222-22-2-222-2-22000000000000-222-22-2-22000000000000
χ85444-4-44-4-444-4-4-4-4440044-4-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ86444-4-44-4-4-4-44444-4-40044-4-40000000000000000000000000000000000000000000000000000000000000000000000000000
χ8744-4-44-4-4400004i−4i−4i4i000000002222−22−22−22−222222−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000000000000000000000000000
χ8844-4-44-4-4400004i−4i−4i4i00000000−22−2222222222−22−222i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000000000000000000000000000
χ8944-4-44-4-440000−4i4i4i−4i000000002222−22−22−22−2222222i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000000000000000000000000000
χ9044-4-44-4-440000−4i4i4i−4i00000000−22−2222222222−22−22−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000000000000000000000000000
χ914-444-4-4-444i−4i−4i4i00000000000022−2222−22−2222−2222−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000000000000000000000000000
χ924-444-4-4-444i−4i−4i4i000000000000−2222−222222−2222−222i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000000000000000000000000000
χ934-444-4-4-44−4i4i4i−4i00000000000022−2222−22−2222−22222i2−2i22i2−2i2−2i22i2−2i22i20000000000000000000000000000000000000000000000000000000000
χ944-444-4-4-44−4i4i4i−4i000000000000−2222−222222−2222−22−2i22i2−2i22i22i2−2i22i2−2i20000000000000000000000000000000000000000000000000000000000
χ954-4-4444-4-400000000004-4-44004i−4i−4i4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000
χ964-4-4444-4-400000000004-4-4400−4i4i4i−4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000
χ974-4-4444-4-40000000000-444-400000000004i−4i−4i4i−4i4i4i−4i0000000000000000000000000000000000000000000000000000000000
χ984-4-4444-4-40000000000-444-40000000000−4i4i4i−4i4i−4i−4i4i0000000000000000000000000000000000000000000000000000000000

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