Finite Group Databasebeta

← Group #11780011

Character table — Group #11780011

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222222444444444444444888888888888812121212121212121212121212121212121212121212121216161616161624242424242448484872727272
order1222334444666666346661212121212121212121244121212121212121212121244448888121212121212121224242424242424241212121212124412121212412128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111-1-11-1-1-1-111111111-1-111111111-1-1-1-111111111-1-1-1-1-1-11-111-1-1-1-1-111-1-1
χ61111111111111111111111111111111-1-11-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1111-1-111
χ71111111111111111111111111111111-1-11-1-1-1-1111111-1-1111111-1-1-1-1111111111111-1-1-1-1-1-1-11-1-111-1-1-1-1-111
χ81111111111111111111111111111111-1-11-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111111-1-1
χ92222222-22-22222222-22222222-2-2-2-2-2-200-2000022-2-2-2-2220000002222000000000000000000-20-2-2000000000
χ102222222-22-22222222-22222222-2-2-2-2-2-200-2000022-2-2-2-2-2-2000000-2-2-2-20000000000000000002022000000000
χ11222222-22-222222222-2222-2-2-2-22222-2-200-20000-2-222-2-20022000000002222000000000000000-200-2-20000000
χ12222222-22-222222222-2222-2-2-2-22222-2-200-20000-2-222-2-200-2-200000000-2-2-2-2000000000000000200220000000
χ13222222-2-2-2-222222222222-2-2-2-2-2-2-2-2222-2222-2-2-2-2-2-2220000000000000000000000002-222-2-20000000000000
χ14222222-2-2-2-222222222222-2-2-2-2-2-2-2-222-222-2-222-2-2-2-222000000000000000000000000-22-2-2220000000000000
χ1522222-1222222-1-12-1-12-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-10000000022-1-1-1-122-1-1-1-10000000
χ1622222-1222222-1-12-1-12-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000111111110000000022-1-1-1-1-2-211110000000
χ1722222-1222222-1-12-1-12-1-1-122-1-1-1-12222-2-2-11111-1-1-1-1-1-122-2-20000-1-1-1-1111100000000-2-211112-2-1-1110000000
χ1822222-1222222-1-12-1-12-1-1-122-1-1-1-12222-2-2-11111-1-1-1-1-1-1-2-22200001111-1-1-1-100000000-2-21111-2211-1-10000000
χ1922222-12-22-222-1-12-1-1-2-1-1-122-1-111-2-2-2-2001−i3i3−i3i3-1-1111122000000-1-1-1-1−i3−i3i3i30000000000−i3i3−i3i3-2011−i3i30000000
χ2022222-12-22-222-1-12-1-1-2-1-1-122-1-111-2-2-2-2001−i3i3−i3i3-1-11111-2-20000001111i3i3−i3−i30000000000−i3i3−i3i320-1-1i3−i30000000
χ2122222-12-22-222-1-12-1-1-2-1-1-122-1-111-2-2-2-2001i3−i3i3−i3-1-1111122000000-1-1-1-1i3i3−i3−i30000000000i3−i3i3−i3-2011i3−i30000000
χ2222222-12-22-222-1-12-1-1-2-1-1-122-1-111-2-2-2-2001i3−i3i3−i3-1-11111-2-20000001111−i3−i3i3i30000000000i3−i3i3−i320-1-1−i3i30000000
χ2322222-1-22-2222-1-12-1-1-2-1-1-1-2-211-1-122-2-2001−i3i3i3−i311-1-11100220000−i3−i3i3i3-1-1-1-10000000000−i3i3i3−i30-2−i3i3110000000
χ2422222-1-22-2222-1-12-1-1-2-1-1-1-2-211-1-122-2-2001−i3i3i3−i311-1-11100-2-20000i3i3−i3−i311110000000000−i3i3i3−i302i3−i3-1-10000000
χ2522222-1-22-2222-1-12-1-1-2-1-1-1-2-211-1-122-2-2001i3−i3−i3i311-1-11100220000i3i3−i3−i3-1-1-1-10000000000i3−i3−i3i30-2i3−i3110000000
χ2622222-1-22-2222-1-12-1-1-2-1-1-1-2-211-1-122-2-2001i3−i3−i3i311-1-11100-2-20000−i3−i3i3i311110000000000i3−i3−i3i302−i3i3-1-10000000
χ2722222-1-2-2-2-222-1-12-1-12-1-1-1-2-21111-2-2222-2-1-1-1111111-1-100000000−i3−i3i3i3−i3−i3i3i3000000002-2-1-11100i3−i3i3−i30000000
χ2822222-1-2-2-2-222-1-12-1-12-1-1-1-2-21111-2-2222-2-1-1-1111111-1-100000000i3i3−i3−i3i3i3−i3−i3000000002-2-1-11100−i3i3−i3i30000000
χ2922222-1-2-2-2-222-1-12-1-12-1-1-1-2-21111-2-222-22-111-1-11111-1-100000000−i3−i3i3i3i3i3−i3−i300000000-2211-1-100i3−i3−i3i30000000
χ3022222-1-2-2-2-222-1-12-1-12-1-1-1-2-21111-2-222-22-111-1-11111-1-100000000i3i3−i3−i3−i3−i3i3i300000000-2211-1-100−i3i3i3−i30000000
χ312222-122222-1-122-12-12-1-1-1-1-12222-1-1-1-12222222-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-1-10000
χ322222-122222-1-122-12-12-1-1-1-1-12222-1-1-1-12222222-1-1-1-1-1-10000-2-2-2-20000000011111111-1-1-1-1-1-1000000-2110000
χ332222-122222-1-122-12-12-1-1-1-1-12222-1-1-1-1-2-22-2-2-2-2-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1111111000000-2110000
χ342222-122222-1-122-12-12-1-1-1-1-12222-1-1-1-1-2-22-2-2-2-2-1-1-1-1-1-10000-2-2-2-200000000111111111111110000002-1-10000
χ352222-12-2-2-2-2-1-122-12-12-1-1-111-2-2-2-211-1-12-2222-2-21111-1-10000000000000000−i3−i3−i3−i3i3i3i3i3-11-1-1110000000−i3i30000
χ362222-12-2-2-2-2-1-122-12-12-1-1-111-2-2-2-211-1-12-2222-2-21111-1-10000000000000000i3i3i3i3−i3−i3−i3−i3-11-1-1110000000i3−i30000
χ372222-12-2-2-2-2-1-122-12-12-1-1-111-2-2-2-211-1-1-222-2-2221111-1-10000000000000000−i3−i3−i3−i3i3i3i3i31-111-1-10000000i3−i30000
χ382222-12-2-2-2-2-1-122-12-12-1-1-111-2-2-2-211-1-1-222-2-2221111-1-10000000000000000i3i3i3i3−i3−i3−i3−i31-111-1-10000000−i3i30000
χ3922-2-22220-202-22-2-2-2202-2-22-22-200000000000002-200002-20022−2−22-22-2000022−2−222−2−20000000000000002−200
χ4022-2-22220-202-22-2-2-2202-2-22-22-200000000000002-200002-200−2−2222-22-20000−2−222−2−222000000000000000−2200
χ4122-2-22220-202-22-2-2-2202-2-22-22-200000000000002-20000-220022−2−2-22-22000022−2−222−2−2000000000000000−2200
χ4222-2-22220-202-22-2-2-2202-2-22-22-200000000000002-20000-2200−2−222-22-220000−2−222−2−2220000000000000002−200
χ432-2-22220-202-2-2-222-220-22-200002-22-2000000000002-200002-2−i2i2−i2i200002-22-2−i2i2−i2i2−i2i2−i2i200000000000000000−i2i2
χ442-2-22220-202-2-2-222-220-22-200002-22-2000000000002-200002-2i2−i2i2−i200002-22-2i2−i2i2−i2i2−i2i2−i200000000000000000i2−i2
χ452-2-22220-202-2-2-222-220-22-200002-22-2000000000002-20000-22−i2i2−i2i20000-22-22−i2i2−i2i2−i2i2−i2i200000000000000000i2−i2
χ462-2-22220-202-2-2-222-220-22-200002-22-2000000000002-20000-22i2−i2i2−i20000-22-22i2−i2i2−i2i2−i2i2−i200000000000000000−i2i2
χ474444-244-44-4-2-244-24-2-4-2-2-2-2-244-4-4222200-40000-2-222220000000000000000000000000000000000000000000
χ484444-24-44-44-2-244-24-2-4-2-2-222-4-444-2-22200-4000022-2-2220000000000000000000000000000000000000000000
χ494444-2-24444-2-2-2-2-2-214111-2-2-2-2-2-2-2-2-2-244-2-2-2-2-2111111000000000000000000000000-2-211110000000000000
χ504444-2-24444-2-2-2-2-2-214111-2-2-2-2-2-2-2-2-2-2-4-4-2222211111100000000000000000000000022-1-1-1-10000000000000
χ514444-2-24-44-4-2-2-2-2-2-21-4111-2-2-2-2222222002−2i32i3−2i32i311-1-1-1-100000000000000000000000000i3−i3i3−i30000000000000
χ524444-2-24-44-4-2-2-2-2-2-21-4111-2-2-2-22222220022i3−2i32i3−2i311-1-1-1-100000000000000000000000000−i3i3−i3i30000000000000
χ534444-2-2-44-44-2-2-2-2-2-21-41112222-2-2-2-222002−2i32i32i3−2i3-1-111-1-100000000000000000000000000i3−i3−i3i30000000000000
χ544444-2-2-44-44-2-2-2-2-2-21-41112222-2-2-2-2220022i3−2i3−2i32i3-1-111-1-100000000000000000000000000−i3i3i3−i30000000000000
χ554444-2-2-4-4-4-4-2-2-2-2-2-21411122222222-2-24-4-2-2-222-1-1-1-111000000000000000000000000-2211-1-10000000000000
χ564444-2-2-4-4-4-4-2-2-2-2-2-21411122222222-2-2-44-222-2-2-1-1-1-1110000000000000000000000002-2-1-1110000000000000
χ5744-4-444-40404-44-4-4-4404-4-4-44-440000000000000-4400000000000000000000000000000000000000000000000
χ5844-4-44-240-404-4-22-42-20-2224-4-220000000000000-2200004-4000000-22-220000000000000000000000000000000
χ5944-4-44-240-404-4-22-42-20-2224-4-220000000000000-220000-440000002-22-20000000000000000000000000000000
χ6044-4-44-2-40404-4-22-42-20-222-442-200000000000002-2000000000000−2i32i32i3−2i30000000000000000000000000000000
χ6144-4-44-2-40404-4-22-42-20-222-442-200000000000002-20000000000002i3−2i3−2i32i30000000000000000000000000000000
χ6244-4-4-2440-40-224-42-4-20-222-224-40000000000000-22000000002222−22−2200000000−2−222−2−2220000000000000000000
χ6344-4-4-2440-40-224-42-4-20-222-224-40000000000000-2200000000−22−2222220000000022−2−222−2−20000000000000000000
χ6444-4-4-24-4040-224-42-4-20-2222-2-4400000000000002-200000000000000000000i6i6−i6−i6−i6−i6i6i60000000000000000000
χ6544-4-4-24-4040-224-42-4-20-2222-2-4400000000000002-200000000000000000000−i6−i6i6i6i6i6−i6−i60000000000000000000
χ664-44-4440000-44-4-4-4440-4-440000000000000000000000000002i−2i−2i2i000000002i−2i−2i2i2i−2i−2i2i0000000000000000000
χ674-44-4440000-44-4-4-4440-4-44000000000000000000000000000−2i2i2i−2i00000000−2i2i2i−2i−2i2i2i−2i0000000000000000000
χ684-44-4-2400002-2-4-424-2022-200000000−2i32i300000000000−2i32i300002i−2i−2i2i000000002ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ220000000000000000000
χ694-44-4-2400002-2-4-424-2022-200000000−2i32i300000000000−2i32i30000−2i2i2i−2i00000000−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ220000000000000000000
χ704-44-4-2400002-2-4-424-2022-2000000002i3−2i3000000000002i3−2i300002i−2i−2i2i000000002ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ140000000000000000000
χ714-44-4-2400002-2-4-424-2022-2000000002i3−2i3000000000002i3−2i30000−2i2i2i−2i00000000−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ140000000000000000000
χ724-4-4444040-4-4-4-444-440-44-40000-44-4400000000000-44000000000000000000000000000000000000000000000
χ734-4-444-2040-4-4-42-242-202-2200002-2-44000000000002-200000000000000−2i32i32i3−2i3000000000000000000000000000
χ744-4-444-2040-4-4-42-242-202-2200002-2-44000000000002-2000000000000002i3−2i3−2i32i3000000000000000000000000000
χ754-4-444-20-404-4-42-242-202-220000-224-400000000000-2200004-400000000-22-22000000000000000000000000000
χ764-4-444-20-404-4-42-242-202-220000-224-400000000000-220000-44000000002-22-2000000000000000000000000000
χ774-4-44-24040-422-44-2-4-202-220000-442-2000000000002-20000000000000000006−66−6−66−660000000000000000000
χ784-4-44-24040-422-44-2-4-202-220000-442-2000000000002-2000000000000000000−66−666−66−60000000000000000000
χ794-4-44-240-40422-44-2-4-202-2200004-4-2200000000000-22000000−2i22i2−2i22i200000000i2−i2i2−i2i2−i2i2−i20000000000000000000
χ804-4-44-240-40422-44-2-4-202-2200004-4-2200000000000-220000002i2−2i22i2−2i200000000−i2i2−i2i2−i2i2−i2i20000000000000000000
χ8188-8-8-4-480-80-44-4444202-2-2-44-4400000000000002-200000000000000000000000000000000000000000000000
χ8288-8-8-4-4-8080-44-4444202-2-24-44-40000000000000-2200000000000000000000000000000000000000000000000
χ838-88-88-40000-8844-8-4-4044-4000000000000000000000000000000000000000000000000000000000000000000
χ848-88-8-4-400004-4444-420-2-2200000000−4i34i3000000000002i3−2i30000000000000000000000000000000000000000000
χ858-88-8-4-400004-4444-420-2-22000000004i3−4i300000000000−2i32i30000000000000000000000000000000000000000000
χ868-8-88-4-4080-8444-4-4420-22-200004-44-400000000000-22000000000000000000000000000000000000000000000
χ878-8-88-4-40-808444-4-4420-22-20000-44-44000000000002-2000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.