Finite Group Databasebeta

← Group #481452

Character table — Group #481452

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11112244448888888888888111122444488888888888881111224444888888888888811112244448888888888888
order12222244442244488888888222222444422444888888882222224444224448888888822222244442244488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1
χ31111111111-1-11-1-11111-1-1-1-11111111111-1-11-1-11111-1-1-1-11111111111-1-11-1-11111-1-1-1-11111111111-1-11-1-11111-1-1-1-1
χ41111111111-1-11-1-1-1-1-1-111111111111111-1-11-1-1-1-1-1-111111111111111-1-11-1-1-1-1-1-111111111111111-1-11-1-1-1-1-1-11111
χ5111111-1-1-1-1111-1-1ii−i−iii−i−i111111-1-1-1-1111-1-1ii−i−iii−i−i111111-1-1-1-1111-1-1ii−i−iii−i−i111111-1-1-1-1111-1-1ii−i−iii−i−i
χ6111111-1-1-1-1111-1-1−i−iii−i−iii111111-1-1-1-1111-1-1−i−iii−i−iii111111-1-1-1-1111-1-1−i−iii−i−iii111111-1-1-1-1111-1-1−i−iii−i−iii
χ7111111-1-1-1-1-1-1111ii−i−i−i−iii111111-1-1-1-1-1-1111ii−i−i−i−iii111111-1-1-1-1-1-1111ii−i−i−i−iii111111-1-1-1-1-1-1111ii−i−i−i−iii
χ8111111-1-1-1-1-1-1111−i−iiiii−i−i111111-1-1-1-1-1-1111−i−iiiii−i−i111111-1-1-1-1-1-1111−i−iiiii−i−i111111-1-1-1-1-1-1111−i−iiiii−i−i
χ92222222-2-2200-200000000002222222-2-2200-200000000002222222-2-2200-200000000002222222-2-2200-20000000000
χ10222222-222-200-20000000000222222-222-200-20000000000222222-222-200-20000000000222222-222-200-20000000000
χ112-22-22-202i−2i00000000001+i−1−i1−i−1+i2-22-22-202i−2i00000000001+i−1−i1−i−1+i2-22-22-202i−2i00000000001+i−1−i1−i−1+i2-22-22-202i−2i00000000001+i−1−i1−i−1+i
χ122-22-22-202i−2i0000000000−1−i1+i−1+i1−i2-22-22-202i−2i0000000000−1−i1+i−1+i1−i2-22-22-202i−2i0000000000−1−i1+i−1+i1−i2-22-22-202i−2i0000000000−1−i1+i−1+i1−i
χ132-22-22-20−2i2i00000000001−i−1+i1+i−1−i2-22-22-20−2i2i00000000001−i−1+i1+i−1−i2-22-22-20−2i2i00000000001−i−1+i1+i−1−i2-22-22-20−2i2i00000000001−i−1+i1+i−1−i
χ142-22-22-20−2i2i0000000000−1+i1−i−1−i1+i2-22-22-20−2i2i0000000000−1+i1−i−1−i1+i2-22-22-20−2i2i0000000000−1+i1−i−1−i1+i2-22-22-20−2i2i0000000000−1+i1−i−1−i1+i
χ152-22-2-22200-200000i2−i2i2−i200002-22-2-22200-200000i2−i2i2−i200002-22-2-22200-200000i2−i2i2−i200002-22-2-22200-200000i2−i2i2−i20000
χ162-22-2-22200-200000−i2i2−i2i200002-22-2-22200-200000−i2i2−i2i200002-22-2-22200-200000−i2i2−i2i200002-22-2-22200-200000−i2i2−i2i20000
χ172-22-2-22-2002000002−2−2200002-22-2-22-2002000002−2−2200002-22-2-22-2002000002−2−2200002-22-2-22-2002000002−2−220000
χ182-22-2-22-200200000−222−200002-22-2-22-200200000−222−200002-22-2-22-200200000−222−200002-22-2-22-200200000−222−20000
χ194444-4-4000000000000000004444-4-4000000000000000004444-4-4000000000000000004444-4-400000000000000000
χ2044-4-40000000002i−2i0000000044-4-40000000002i−2i0000000044-4-40000000002i−2i0000000044-4-40000000002i−2i00000000
χ2144-4-4000000000−2i2i0000000044-4-4000000000−2i2i0000000044-4-4000000000−2i2i0000000044-4-4000000000−2i2i00000000
χ224-4-440000002-2000000000004-4-440000002-2000000000004-4-440000002-2000000000004-4-440000002-200000000000
χ234-4-44000000-22000000000004-4-44000000-22000000000004-4-44000000-22000000000004-4-44000000-2200000000000
χ2411111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ25111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ261111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-11111
χ271111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-11111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1
χ28111111-1-1-1-1111-1-1ii−i−iii−i−i-1-1-1-1-1-11111-1-1-111−i−iii−i−iii111111-1-1-1-1111-1-1ii−i−iii−i−i-1-1-1-1-1-11111-1-1-111−i−iii−i−iii
χ29111111-1-1-1-1111-1-1−i−iii−i−iii-1-1-1-1-1-11111-1-1-111ii−i−iii−i−i111111-1-1-1-1111-1-1−i−iii−i−iii-1-1-1-1-1-11111-1-1-111ii−i−iii−i−i
χ30111111-1-1-1-1-1-1111ii−i−i−i−iii-1-1-1-1-1-1111111-1-1-1−i−iiiii−i−i111111-1-1-1-1-1-1111ii−i−i−i−iii-1-1-1-1-1-1111111-1-1-1−i−iiiii−i−i
χ31111111-1-1-1-1-1-1111−i−iiiii−i−i-1-1-1-1-1-1111111-1-1-1ii−i−i−i−iii111111-1-1-1-1-1-1111−i−iiiii−i−i-1-1-1-1-1-1111111-1-1-1ii−i−i−i−iii
χ322222222-2-2200-20000000000-2-2-2-2-2-2-222-200200000000002222222-2-2200-20000000000-2-2-2-2-2-2-222-20020000000000
χ33222222-222-200-20000000000-2-2-2-2-2-22-2-220020000000000222222-222-200-20000000000-2-2-2-2-2-22-2-220020000000000
χ342-22-22-202i−2i00000000001+i−1−i1−i−1+i-22-22-220−2i2i0000000000−1−i1+i−1+i1−i2-22-22-202i−2i00000000001+i−1−i1−i−1+i-22-22-220−2i2i0000000000−1−i1+i−1+i1−i
χ352-22-22-202i−2i0000000000−1−i1+i−1+i1−i-22-22-220−2i2i00000000001+i−1−i1−i−1+i2-22-22-202i−2i0000000000−1−i1+i−1+i1−i-22-22-220−2i2i00000000001+i−1−i1−i−1+i
χ362-22-22-20−2i2i00000000001−i−1+i1+i−1−i-22-22-2202i−2i0000000000−1+i1−i−1−i1+i2-22-22-20−2i2i00000000001−i−1+i1+i−1−i-22-22-2202i−2i0000000000−1+i1−i−1−i1+i
χ372-22-22-20−2i2i0000000000−1+i1−i−1−i1+i-22-22-2202i−2i00000000001−i−1+i1+i−1−i2-22-22-20−2i2i0000000000−1+i1−i−1−i1+i-22-22-2202i−2i00000000001−i−1+i1+i−1−i
χ382-22-2-22200-200000i2−i2i2−i20000-22-222-2-200200000−i2i2−i2i200002-22-2-22200-200000i2−i2i2−i20000-22-222-2-200200000−i2i2−i2i20000
χ392-22-2-22200-200000−i2i2−i2i20000-22-222-2-200200000i2−i2i2−i200002-22-2-22200-200000−i2i2−i2i20000-22-222-2-200200000i2−i2i2−i20000
χ402-22-2-22-2002000002−2−220000-22-222-2200-200000−222−200002-22-2-22-2002000002−2−220000-22-222-2200-200000−222−20000
χ412-22-2-22-200200000−222−20000-22-222-2200-2000002−2−2200002-22-2-22-200200000−222−20000-22-222-2200-2000002−2−220000
χ424444-4-400000000000000000-4-4-4-444000000000000000004444-4-400000000000000000-4-4-4-44400000000000000000
χ4344-4-40000000002i−2i00000000-4-444000000000−2i2i0000000044-4-40000000002i−2i00000000-4-444000000000−2i2i00000000
χ4444-4-4000000000−2i2i00000000-4-4440000000002i−2i0000000044-4-4000000000−2i2i00000000-4-4440000000002i−2i00000000
χ454-4-440000002-200000000000-444-4000000-22000000000004-4-440000002-200000000000-444-4000000-2200000000000
χ464-4-44000000-2200000000000-444-40000002-2000000000004-4-44000000-2200000000000-444-40000002-200000000000
χ471111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ48111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ491111111111-1-11-1-11111-1-1-1-11111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-111-1-1-1-11111
χ501111111111-1-11-1-1-1-1-1-111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1
χ51111111-1-1-1-1111-1-1ii−i−iii−i−i111111-1-1-1-1111-1-1ii−i−iii−i−i-1-1-1-1-1-11111-1-1-111−i−iii−i−iii-1-1-1-1-1-11111-1-1-111−i−iii−i−iii
χ52111111-1-1-1-1111-1-1−i−iii−i−iii111111-1-1-1-1111-1-1−i−iii−i−iii-1-1-1-1-1-11111-1-1-111ii−i−iii−i−i-1-1-1-1-1-11111-1-1-111ii−i−iii−i−i
χ53111111-1-1-1-1-1-1111ii−i−i−i−iii111111-1-1-1-1-1-1111ii−i−i−i−iii-1-1-1-1-1-1111111-1-1-1−i−iiiii−i−i-1-1-1-1-1-1111111-1-1-1−i−iiiii−i−i
χ54111111-1-1-1-1-1-1111−i−iiiii−i−i111111-1-1-1-1-1-1111−i−iiiii−i−i-1-1-1-1-1-1111111-1-1-1ii−i−i−i−iii-1-1-1-1-1-1111111-1-1-1ii−i−i−i−iii
χ552222222-2-2200-200000000002222222-2-2200-20000000000-2-2-2-2-2-2-222-20020000000000-2-2-2-2-2-2-222-20020000000000
χ56222222-222-200-20000000000222222-222-200-20000000000-2-2-2-2-2-22-2-220020000000000-2-2-2-2-2-22-2-220020000000000
χ572-22-22-202i−2i00000000001+i−1−i1−i−1+i2-22-22-202i−2i00000000001+i−1−i1−i−1+i-22-22-220−2i2i0000000000−1−i1+i−1+i1−i-22-22-220−2i2i0000000000−1−i1+i−1+i1−i
χ582-22-22-202i−2i0000000000−1−i1+i−1+i1−i2-22-22-202i−2i0000000000−1−i1+i−1+i1−i-22-22-220−2i2i00000000001+i−1−i1−i−1+i-22-22-220−2i2i00000000001+i−1−i1−i−1+i
χ592-22-22-20−2i2i00000000001−i−1+i1+i−1−i2-22-22-20−2i2i00000000001−i−1+i1+i−1−i-22-22-2202i−2i0000000000−1+i1−i−1−i1+i-22-22-2202i−2i0000000000−1+i1−i−1−i1+i
χ602-22-22-20−2i2i0000000000−1+i1−i−1−i1+i2-22-22-20−2i2i0000000000−1+i1−i−1−i1+i-22-22-2202i−2i00000000001−i−1+i1+i−1−i-22-22-2202i−2i00000000001−i−1+i1+i−1−i
χ612-22-2-22200-200000i2−i2i2−i200002-22-2-22200-200000i2−i2i2−i20000-22-222-2-200200000−i2i2−i2i20000-22-222-2-200200000−i2i2−i2i20000
χ622-22-2-22200-200000−i2i2−i2i200002-22-2-22200-200000−i2i2−i2i20000-22-222-2-200200000i2−i2i2−i20000-22-222-2-200200000i2−i2i2−i20000
χ632-22-2-22-2002000002−2−2200002-22-2-22-2002000002−2−220000-22-222-2200-200000−222−20000-22-222-2200-200000−222−20000
χ642-22-2-22-200200000−222−200002-22-2-22-200200000−222−20000-22-222-2200-2000002−2−220000-22-222-2200-2000002−2−220000
χ654444-4-4000000000000000004444-4-400000000000000000-4-4-4-44400000000000000000-4-4-4-44400000000000000000
χ6644-4-40000000002i−2i0000000044-4-40000000002i−2i00000000-4-444000000000−2i2i00000000-4-444000000000−2i2i00000000
χ6744-4-4000000000−2i2i0000000044-4-4000000000−2i2i00000000-4-4440000000002i−2i00000000-4-4440000000002i−2i00000000
χ684-4-440000002-2000000000004-4-440000002-200000000000-444-4000000-2200000000000-444-4000000-2200000000000
χ694-4-44000000-22000000000004-4-44000000-2200000000000-444-40000002-200000000000-444-40000002-200000000000
χ7011111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111
χ71111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-1
χ721111111111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-111-1-1-1-111111111111111-1-11-1-11111-1-1-1-1
χ731111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-11111111111-1-11-1-1-1-1-1-11111
χ74111111-1-1-1-1111-1-1ii−i−iii−i−i-1-1-1-1-1-11111-1-1-111−i−iii−i−iii-1-1-1-1-1-11111-1-1-111−i−iii−i−iii111111-1-1-1-1111-1-1ii−i−iii−i−i
χ75111111-1-1-1-1111-1-1−i−iii−i−iii-1-1-1-1-1-11111-1-1-111ii−i−iii−i−i-1-1-1-1-1-11111-1-1-111ii−i−iii−i−i111111-1-1-1-1111-1-1−i−iii−i−iii
χ76111111-1-1-1-1-1-1111ii−i−i−i−iii-1-1-1-1-1-1111111-1-1-1−i−iiiii−i−i-1-1-1-1-1-1111111-1-1-1−i−iiiii−i−i111111-1-1-1-1-1-1111ii−i−i−i−iii
χ77111111-1-1-1-1-1-1111−i−iiiii−i−i-1-1-1-1-1-1111111-1-1-1ii−i−i−i−iii-1-1-1-1-1-1111111-1-1-1ii−i−i−i−iii111111-1-1-1-1-1-1111−i−iiiii−i−i
χ782222222-2-2200-20000000000-2-2-2-2-2-2-222-20020000000000-2-2-2-2-2-2-222-200200000000002222222-2-2200-20000000000
χ79222222-222-200-20000000000-2-2-2-2-2-22-2-220020000000000-2-2-2-2-2-22-2-220020000000000222222-222-200-20000000000
χ802-22-22-202i−2i00000000001+i−1−i1−i−1+i-22-22-220−2i2i0000000000−1−i1+i−1+i1−i-22-22-220−2i2i0000000000−1−i1+i−1+i1−i2-22-22-202i−2i00000000001+i−1−i1−i−1+i
χ812-22-22-202i−2i0000000000−1−i1+i−1+i1−i-22-22-220−2i2i00000000001+i−1−i1−i−1+i-22-22-220−2i2i00000000001+i−1−i1−i−1+i2-22-22-202i−2i0000000000−1−i1+i−1+i1−i
χ822-22-22-20−2i2i00000000001−i−1+i1+i−1−i-22-22-2202i−2i0000000000−1+i1−i−1−i1+i-22-22-2202i−2i0000000000−1+i1−i−1−i1+i2-22-22-20−2i2i00000000001−i−1+i1+i−1−i
χ832-22-22-20−2i2i0000000000−1+i1−i−1−i1+i-22-22-2202i−2i00000000001−i−1+i1+i−1−i-22-22-2202i−2i00000000001−i−1+i1+i−1−i2-22-22-20−2i2i0000000000−1+i1−i−1−i1+i
χ842-22-2-22200-200000i2−i2i2−i20000-22-222-2-200200000−i2i2−i2i20000-22-222-2-200200000−i2i2−i2i200002-22-2-22200-200000i2−i2i2−i20000
χ852-22-2-22200-200000−i2i2−i2i20000-22-222-2-200200000i2−i2i2−i20000-22-222-2-200200000i2−i2i2−i200002-22-2-22200-200000−i2i2−i2i20000
χ862-22-2-22-2002000002−2−220000-22-222-2200-200000−222−20000-22-222-2200-200000−222−200002-22-2-22-2002000002−2−220000
χ872-22-2-22-200200000−222−20000-22-222-2200-2000002−2−220000-22-222-2200-2000002−2−2200002-22-2-22-200200000−222−20000
χ884444-4-400000000000000000-4-4-4-44400000000000000000-4-4-4-444000000000000000004444-4-400000000000000000
χ8944-4-40000000002i−2i00000000-4-444000000000−2i2i00000000-4-444000000000−2i2i0000000044-4-40000000002i−2i00000000
χ9044-4-4000000000−2i2i00000000-4-4440000000002i−2i00000000-4-4440000000002i−2i0000000044-4-4000000000−2i2i00000000
χ914-4-440000002-200000000000-444-4000000-2200000000000-444-4000000-22000000000004-4-440000002-200000000000
χ924-4-44000000-2200000000000-444-40000002-200000000000-444-40000002-2000000000004-4-44000000-2200000000000

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