Finite Group Databasebeta

← Group #243307

Character table — Group #243307

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111111111111222222222222222244444444444444444444888888888888888888888888888888881616161616161616
order12222222444444444444444444444444444488888888888888882244444488888888888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-111
χ1722222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-200000000000000002222-2-2-2-200000000000000000000000000000000
χ1822222222222222222222-2-2-2-2-2-22222-2-2-2-2-2-20000000000000000-2-2-2-2222200000000000000000000000000000000
χ192222222222222222-2-2-2-2222222-2-2-2-222-2-2-2-222222222-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ202222222222222222-2-2-2-2222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ212222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000002i2i−2i−2i2i2i−2i−2i00000000
χ222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000−2i−2i2i2i−2i−2i2i2i00000000
χ2322222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222-2-200000000000000000000000000000000000000002i2i−2i−2i−2i−2i2i2i00000000
χ2422222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-222-2-20000000000000000000000000000000000000000−2i−2i2i2i2i2i−2i−2i00000000
χ2522222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2-2-222-2-2222222-2-2-2-2-2-2-2-222220000000000000000000000000000000000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2-2-222-2-222-2-2-2-222222222-2-2-2-20000000000000000000000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2-2-222000000000000000022-2-2-2-22200000000000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22222-2-2-2-2220000000000000000-2-22222-2-200000000000000000000000000000000
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χ3222-2-22-22-22i2i2i2i−2i−2i−2i−2i00002i2i−2i−2i2-200002-20000-2-222−2i−2i2i2i0000000000000000−i2−i2i2i2−2−222i2i2−i2−i222−2−20000000000000000
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χ3422-2-22-22-2−2i−2i−2i−2i2i2i2i2i0000−2i−2i2i2i2-200002-2000022-2-2−2i−2i2i2i0000000000000000−i2−i2i2i222−2−2−i2−i2i2i222−2−20000000000000000
χ3522-2-22-22-2−2i−2i−2i−2i2i2i2i2i0000−2i−2i2i2i2-200002-20000-2-2222i2i−2i−2i0000000000000000i2i2−i2−i2−2−222−i2−i2i2i222−2−20000000000000000
χ3622-2-22-22-2−2i−2i−2i−2i2i2i2i2i0000−2i−2i2i2i2-200002-20000-2-2222i2i−2i−2i0000000000000000−i2−i2i2i222−2−2i2i2−i2−i2−2−2220000000000000000
χ372-22-22-2-222i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000022-2-2000000i2−i2i2−i22−22−2i2i2−i2−i222−2−200002i−2i2-200000000000000002−22−2i2−i2i2−i200000000
χ382-22-22-2-222i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000022-2-2000000i2−i2i2−i22−22−2i2i2−i2−i222−2−20000−2i2i-220000000000000000−22−22−i2i2−i2i200000000
χ392-22-22-2-222i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000022-2-2000000−i2i2−i2i2−22−22−i2−i2i2i2−2−22200002i−2i2-20000000000000000−22−22−i2i2−i2i200000000
χ402-22-22-2-222i2i−2i−2i2i2i−2i−2i2i2i−2i−2i00000022-2-2000000−i2i2−i2i2−22−22−i2−i2i2i2−2−2220000−2i2i-2200000000000000002−22−2i2−i2i2−i200000000
χ412-22-22-2-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000-2-222000000i2−i2i2−i22−22−2−i2−i2i2i2−2−2222-22i−2i00000000000000000000i2−i2−i2i2−222−200000000
χ422-22-22-2-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000-2-222000000i2−i2i2−i22−22−2−i2−i2i2i2−2−222-22−2i2i00000000000000000000−i2i2i2−i22−2−2200000000
χ432-22-22-2-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000-2-222000000−i2i2−i2i2−22−22i2i2−i2−i222−2−22-22i−2i00000000000000000000−i2i2i2−i22−2−2200000000
χ442-22-22-2-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i000000-2-222000000−i2i2−i2i2−22−22i2i2−i2−i222−2−2-22−2i2i00000000000000000000i2−i2−i2i2−222−200000000
χ452-22-22-2-22−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000-2-222000000i2−i2i2−i2−22−22−i2−i2i2i222−2−22-2−2i2i00000000000000000000i2−i2−i2i22−2−2200000000
χ462-22-22-2-22−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000-2-222000000i2−i2i2−i2−22−22−i2−i2i2i222−2−2-222i−2i00000000000000000000−i2i2i2−i2−222−200000000
χ472-22-22-2-22−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000-2-222000000−i2i2−i2i22−22−2i2i2−i2−i2−2−2222-2−2i2i00000000000000000000−i2i2i2−i2−222−200000000
χ482-22-22-2-22−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i000000-2-222000000−i2i2−i2i22−22−2i2i2−i2−i2−2−222-222i−2i00000000000000000000i2−i2−i2i22−2−2200000000
χ492-22-22-2-22−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000022-2-2000000i2−i2i2−i2−22−22i2i2−i2−i2−2−22200002i−2i-2200000000000000002−22−2−i2i2−i2i200000000
χ502-22-22-2-22−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000022-2-2000000i2−i2i2−i2−22−22i2i2−i2−i2−2−2220000−2i2i2-20000000000000000−22−22i2−i2i2−i200000000
χ512-22-22-2-22−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000022-2-2000000−i2i2−i2i22−22−2−i2−i2i2i222−2−200002i−2i-220000000000000000−22−22i2−i2i2−i200000000
χ522-22-22-2-22−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i00000022-2-2000000−i2i2−i2i22−22−2−i2−i2i2i222−2−20000−2i2i2-200000000000000002−22−2−i2i2−i2i200000000
χ532-22-2-222-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2-22-22-2-222-22i−2i000000000000000000000000000000002i−2i2i−2i2-22-20000000000000000
χ542-22-2-222-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2-22-22-2-222-22i−2i00000000000000000000000000000000−2i2i−2i2i-22-220000000000000000
χ552-22-2-222-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i-222-22-22-2-22−2i2i00000000000000000000000000000000000000000000000000002i−2i2-2
χ562-22-2-222-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i-222-22-22-2-22−2i2i0000000000000000000000000000000000000000000000000000−2i2i-22
χ572-22-2-222-22i−2i2i−2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i2-2-22-22-22-22−2i2i0000000000000000000000002-22-22i−2i2i−2i000000000000000000000000
χ582-22-2-222-22i−2i2i−2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i2-2-22-22-22-22−2i2i000000000000000000000000-22-22−2i2i−2i2i000000000000000000000000
χ592-22-2-222-22i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i-22-22-222-22-22i−2i0000000000000000000000000000000000000000000000002-22i−2i0000
χ602-22-2-222-22i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i-22-22-222-22-22i−2i000000000000000000000000000000000000000000000000-22−2i2i0000
χ612-22-2-222-2−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i-22-22-222-22-2−2i2i0000000000000000000000000000000000000000000000002-2−2i2i0000
χ622-22-2-222-2−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i-22-22-222-22-2−2i2i000000000000000000000000000000000000000000000000-222i−2i0000
χ632-22-2-222-2−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2-2-22-22-22-222i−2i0000000000000000000000002-22-2−2i2i−2i2i000000000000000000000000
χ642-22-2-222-2−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2-2-22-22-22-222i−2i000000000000000000000000-22-222i−2i2i−2i000000000000000000000000
χ652-22-2-222-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i-222-22-22-2-222i−2i00000000000000000000000000000000000000000000000000002i−2i-22
χ662-22-2-222-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i-222-22-22-2-222i−2i0000000000000000000000000000000000000000000000000000−2i2i2-2
χ672-22-2-222-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2-22-22-2-222-2−2i2i000000000000000000000000000000002i−2i2i−2i-22-220000000000000000
χ682-22-2-222-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2-22-22-2-222-2−2i2i00000000000000000000000000000000−2i2i−2i2i2-22-20000000000000000
χ692-2-22-2-2222-22-2-22-2200002-2-22220000-2-20000000000002i−2i2i−2i2i−2i2i−2i00000000i2−i2−i2i2−i2i2i2−i22−2−222−2−220000000000000000
χ702-2-22-2-2222-22-2-22-2200002-2-22220000-2-20000000000002i−2i2i−2i2i−2i2i−2i00000000−i2i2i2−i2i2−i2−i2i2−222−2−222−20000000000000000
χ712-2-22-2-2222-22-2-22-2200002-2-22220000-2-2000000000000−2i2i−2i2i−2i2i−2i2i00000000i2−i2−i2i2−i2i2i2−i2−222−2−222−20000000000000000
χ722-2-22-2-2222-22-2-22-2200002-2-22220000-2-2000000000000−2i2i−2i2i−2i2i−2i2i00000000−i2i2i2−i2i2−i2−i2i22−2−222−2−220000000000000000
χ732-2-22-2-222-22-222-22-20000-222-2220000-2-20000000000002i−2i2i−2i−2i2i−2i2i00000000i2−i2−i2i2i2−i2−i2i22−2−22−222−20000000000000000
χ742-2-22-2-222-22-222-22-20000-222-2220000-2-20000000000002i−2i2i−2i−2i2i−2i2i00000000−i2i2i2−i2−i2i2i2−i2−222−22−2−220000000000000000
χ752-2-22-2-222-22-222-22-20000-222-2220000-2-2000000000000−2i2i−2i2i2i−2i2i−2i00000000i2−i2−i2i2i2−i2−i2i2−222−22−2−220000000000000000
χ762-2-22-2-222-22-222-22-20000-222-2220000-2-2000000000000−2i2i−2i2i2i−2i2i−2i00000000−i2i2i2−i2−i2i2i2−i22−2−22−222−20000000000000000
χ774444-4-4-4-44-4-444-4-444-4-440000004-4-4400000000000000000000000000000000000000000000000000000000000000
χ784444-4-4-4-44-4-444-4-44-444-4000000-444-400000000000000000000000000000000000000000000000000000000000000
χ794444-4-4-4-4-444-4-444-44-4-44000000-444-400000000000000000000000000000000000000000000000000000000000000
χ804444-4-4-4-4-444-4-444-4-444-40000004-4-4400000000000000000000000000000000000000000000000000000000000000
χ8144-4-44-44-44i4i4i4i−4i−4i−4i−4i0000−4i−4i4i4i-440000-44000000000000000000000000000000000000000000000000000000000000
χ8244-4-44-44-4−4i−4i−4i−4i4i4i4i4i00004i4i−4i−4i-440000-44000000000000000000000000000000000000000000000000000000000000
χ8344-4-4-44-444i−4i−4i4i−4i4i4i−4i000000000000000000000000000022−22−2222−2i22i22i2−2i20000000000000000000000000000000000000000
χ8444-4-4-44-444i−4i−4i4i−4i4i4i−4i0000000000000000000000000000−222222−222i2−2i2−2i22i20000000000000000000000000000000000000000
χ8544-4-4-44-44−4i4i4i−4i4i−4i−4i4i000000000000000000000000000022−22−22222i2−2i2−2i22i20000000000000000000000000000000000000000
χ8644-4-4-44-44−4i4i4i−4i4i−4i−4i4i0000000000000000000000000000−222222−22−2i22i22i2−2i20000000000000000000000000000000000000000
χ874-4-4444-4-444-4-4-4-444000000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ884-4-4444-4-444-4-4-4-44400000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ894-4-4444-4-4-4-44444-4-4000000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000000000000
χ904-4-4444-4-4-4-44444-4-400000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000000000000
χ914-4-44-4-4444-44-4-44-440000-444-4-4-4000044000000000000000000000000000000000000000000000000000000000000
χ924-4-44-4-444-44-444-44-400004-4-44-4-4000044000000000000000000000000000000000000000000000000000000000000

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