Finite Group Databasebeta

← Group #11779726

Character table — Group #11779726

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222222444444444444444888888888888812121212121212121212121212121212121212121212121216161616161624242424242448484872727272
order1222334444666666346661212121212121212121222666612121212121212222266666666888824242424242424246666664412121212412128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1111-1-1-1-1
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
χ51111111111111111111111111111111-1-1-1-1-1-1111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-11-111-1-1-1-1-111-1-1
χ61111111111111111111111111111111-1-1-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1111-1-111
χ71111111111111111111111111111111-1-1-1-1-1-11111111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-11-1-111-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-1-1-11111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111111-1-1
χ92222222-22-22222222-22222222-2-2-2-2-2-2000000-222-2-2-2-20022000022220000000000000000000-200-2-20000000
χ102222222-22-22222222-22222222-2-2-2-2-2-2000000-222-2-2-2-200-2-20000-2-2-2-20000000000000000000200220000000
χ11222222-22-222222222-2222-2-2-2-22222-2-2000000-2-2-222-2-2220022220000000000000000000000-20-2-2000000000
χ12222222-22-222222222-2222-2-2-2-22222-2-2000000-2-2-222-2-2-2-200-2-2-2-200000000000000000000002022000000000
χ13222222-2-2-2-222222222222-2-2-2-2-2-2-2-2222-222-2-22-2-2-2-2220000000000000000000000002-222-2-20000000000000
χ14222222-2-2-2-222222222222-2-2-2-2-2-2-2-222-22-2-2222-2-2-2-222000000000000000000000000-22-2-2220000000000000
χ1522222-1222222-1-1-12-12-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000022-1-1-1-122-1-1-1-10000000
χ1622222-1222222-1-1-12-12-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000022-1-1-1-1-2-211110000000
χ1722222-1222222-1-1-12-12-1-1-122-1-1-1-12222-2-21111-1-1-1-1-1-1-122-2-2-1-1-1-11111000000000000-2-211112-2-1-1110000000
χ1822222-1222222-1-1-12-12-1-1-122-1-1-1-12222-2-21111-1-1-1-1-1-1-1-2-2221111-1-1-1-1000000000000-2-21111-2211-1-10000000
χ1922222-12-22-222-1-1-12-1-2-1-1-122-1-111-2-2-2-200−i3i3−i3i31-1-111110022−i3−i3i3i3-1-1-1-100000000000000−i3i3−i3i30-2−i3i3110000000
χ2022222-12-22-222-1-1-12-1-2-1-1-122-1-111-2-2-2-200−i3i3−i3i31-1-1111100-2-2i3i3−i3−i3111100000000000000−i3i3−i3i302i3−i3-1-10000000
χ2122222-12-22-222-1-1-12-1-2-1-1-122-1-111-2-2-2-200i3−i3i3−i31-1-111110022i3i3−i3−i3-1-1-1-100000000000000i3−i3i3−i30-2i3−i3110000000
χ2222222-12-22-222-1-1-12-1-2-1-1-122-1-111-2-2-2-200i3−i3i3−i31-1-1111100-2-2−i3−i3i3i3111100000000000000i3−i3i3−i302−i3i3-1-10000000
χ2322222-1-22-2222-1-1-12-1-2-1-1-1-2-211-1-122-2-200−i3i3i3−i3111-1-1112200-1-1-1-1−i3−i3i3i300000000000000−i3i3i3−i3-2011−i3i30000000
χ2422222-1-22-2222-1-1-12-1-2-1-1-1-2-211-1-122-2-200−i3i3i3−i3111-1-111-2-2001111i3i3−i3−i300000000000000−i3i3i3−i320-1-1i3−i30000000
χ2522222-1-22-2222-1-1-12-1-2-1-1-1-2-211-1-122-2-200i3−i3−i3i3111-1-1112200-1-1-1-1i3i3−i3−i300000000000000i3−i3−i3i3-2011i3−i30000000
χ2622222-1-22-2222-1-1-12-1-2-1-1-1-2-211-1-122-2-200i3−i3−i3i3111-1-111-2-2001111−i3−i3i3i300000000000000i3−i3−i3i320-1-1−i3i30000000
χ2722222-1-2-2-2-222-1-1-12-12-1-1-1-2-21111-2-2222-2-1-111-11111-1-10000−i3−i3i3i3−i3−i3i3i30000000000002-2-1-11100i3−i3i3−i30000000
χ2822222-1-2-2-2-222-1-1-12-12-1-1-1-2-21111-2-2222-2-1-111-11111-1-10000i3i3−i3−i3i3i3−i3−i30000000000002-2-1-11100−i3i3−i3i30000000
χ2922222-1-2-2-2-222-1-1-12-12-1-1-1-2-21111-2-222-2211-1-1-11111-1-10000−i3−i3i3i3i3i3−i3−i3000000000000-2211-1-100i3−i3−i3i30000000
χ3022222-1-2-2-2-222-1-1-12-12-1-1-1-2-21111-2-222-2211-1-1-11111-1-10000i3i3−i3−i3−i3−i3i3i3000000000000-2211-1-100−i3i3i3−i30000000
χ312222-122222-1-1222-1-12-1-1-1-1-12222-1-1-1-12222222-1-1-1-1-1-10000000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-1-10000
χ322222-122222-1-1222-1-12-1-1-1-1-12222-1-1-1-12222222-1-1-1-1-1-1000000000000-2-2-2-211111111-1-1-1-1-1-1000000-2110000
χ332222-122222-1-1222-1-12-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-22-1-1-1-1-1-10000000000002222-1-1-1-1-1-1-1-1111111000000-2110000
χ342222-122222-1-1222-1-12-1-1-1-1-12222-1-1-1-1-2-2-2-2-2-22-1-1-1-1-1-1000000000000-2-2-2-2111111111111110000002-1-10000
χ352222-12-2-2-2-2-1-1222-1-12-1-1-111-2-2-2-211-1-12-222-2-221111-1-10000000000000000−i3−i3−i3−i3i3i3i3i3-11-1-1110000000−i3i30000
χ362222-12-2-2-2-2-1-1222-1-12-1-1-111-2-2-2-211-1-12-222-2-221111-1-10000000000000000i3i3i3i3−i3−i3−i3−i3-11-1-1110000000i3−i30000
χ372222-12-2-2-2-2-1-1222-1-12-1-1-111-2-2-2-211-1-1-22-2-22221111-1-10000000000000000−i3−i3−i3−i3i3i3i3i31-111-1-10000000i3−i30000
χ382222-12-2-2-2-2-1-1222-1-12-1-1-111-2-2-2-211-1-1-22-2-22221111-1-10000000000000000i3i3i3i3−i3−i3−i3−i31-111-1-10000000−i3i30000
χ392-22-22220-202-2-22-2-2202-2-22-22-200000000000002-20000002-200002-22-2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000000−i2i2
χ402-22-22220-202-2-22-2-2202-2-22-22-200000000000002-20000002-200002-22-2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000000i2−i2
χ412-22-22220-202-2-22-2-2202-2-22-22-200000000000002-2000000-220000-22-22−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000000i2−i2
χ422-22-22220-202-2-22-2-2202-2-22-22-200000000000002-2000000-220000-22-22i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000000−i2i2
χ432-2-22220-202-2-2-2-22220-22-200002-22-2000000000002-2002-2002-22-200002−22−22−22−22−22−20000000000000002−200
χ442-2-22220-202-2-2-2-22220-22-200002-22-2000000000002-2002-2002-22-20000−22−22−22−22−22−22000000000000000−2200
χ452-2-22220-202-2-2-2-22220-22-200002-22-2000000000002-200-2200-22-2200002−22−22−22−22−22−2000000000000000−2200
χ462-2-22220-202-2-2-2-22220-22-200002-22-2000000000002-200-2200-22-220000−22−22−22−22−22−220000000000000002−200
χ474444-244-44-4-2-2444-2-2-4-2-2-2-2-244-4-42222000000-4-2-222220000000000000000000000000000000000000000000
χ484444-24-44-44-2-2444-2-2-4-2-2-222-4-444-2-222000000-422-2-2220000000000000000000000000000000000000000000
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
χ504444-2-24444-2-2-2-2-2-214111-2-2-2-2-2-2-2-2-2-2-4-42222-211111100000000000000000000000022-1-1-1-10000000000000
χ514444-2-24-44-4-2-2-2-2-2-21-4111-2-2-2-222222200−2i32i3−2i32i3211-1-1-1-100000000000000000000000000i3−i3i3−i30000000000000
χ524444-2-24-44-4-2-2-2-2-2-21-4111-2-2-2-2222222002i3−2i32i3−2i3211-1-1-1-100000000000000000000000000−i3i3−i3i30000000000000
χ534444-2-2-44-44-2-2-2-2-2-21-41112222-2-2-2-22200−2i32i32i3−2i32-1-111-1-100000000000000000000000000i3−i3−i3i30000000000000
χ544444-2-2-44-44-2-2-2-2-2-21-41112222-2-2-2-222002i3−2i3−2i32i32-1-111-1-100000000000000000000000000−i3i3i3−i30000000000000
χ554444-2-2-4-4-4-4-2-2-2-2-2-21411122222222-2-24-4-2-222-2-1-1-1-111000000000000000000000000-2211-1-10000000000000
χ564444-2-2-4-4-4-4-2-2-2-2-2-21411122222222-2-2-4422-2-2-2-1-1-1-1110000000000000000000000002-2-1-1110000000000000
χ5744-4-4440000-444-4-4-440-4-44000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i0000000000000000000
χ5844-4-4440000-444-4-4-440-4-4400000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i0000000000000000000
χ5944-4-4-2400002-24-4-42-2022-200000000−2i32i300000000000−2i32i30000000000002i−2i−2i2i2ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ220000000000000000000
χ6044-4-4-2400002-24-4-42-2022-200000000−2i32i300000000000−2i32i3000000000000−2i2i2i−2i−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ220000000000000000000
χ6144-4-4-2400002-24-4-42-2022-2000000002i3−2i3000000000002i3−2i30000000000002i−2i−2i2i2ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ140000000000000000000
χ6244-4-4-2400002-24-4-42-2022-2000000002i3−2i3000000000002i3−2i3000000000000−2i2i2i−2i−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ140000000000000000000
χ634-44-444-40404-4-44-4-4404-4-4-44-440000000000000-4400000000000000000000000000000000000000000000000
χ644-44-44-240-404-42-22-4-20-2224-4-220000000000000-220000004-40000-22-220000000000000000000000000000000
χ654-44-44-240-404-42-22-4-20-2224-4-220000000000000-22000000-4400002-22-20000000000000000000000000000000
χ664-44-44-2-40404-42-22-4-20-222-442-200000000000002-2000000000000−2i32i32i3−2i30000000000000000000000000000000
χ674-44-44-2-40404-42-22-4-20-222-442-200000000000002-20000000000002i3−2i3−2i32i30000000000000000000000000000000
χ684-44-4-2440-40-22-44-42-20-222-224-40000000000000-220000000000000000−2i2−2i22i22i2i2i2−i2−i2i2i2−i2−i20000000000000000000
χ694-44-4-2440-40-22-44-42-20-222-224-40000000000000-2200000000000000002i22i2−2i2−2i2−i2−i2i2i2−i2−i2i2i20000000000000000000
χ704-44-4-24-4040-22-44-42-20-2222-2-4400000000000002-20000000000000000000066−6−6−6−6660000000000000000000
χ714-44-4-24-4040-22-44-42-20-2222-2-4400000000000002-200000000000000000000−6−66666−6−60000000000000000000
χ724-4-4444040-4-4-4-4-44440-44-40000-44-4400000000000-44000000000000000000000000000000000000000000000
χ734-4-444-2040-4-4-422-24-202-2200002-2-44000000000002-2000000−2i32i32i3−2i300000000000000000000000000000000000
χ744-4-444-2040-4-4-422-24-202-2200002-2-44000000000002-20000002i3−2i3−2i32i300000000000000000000000000000000000
χ754-4-444-20-404-4-422-24-202-220000-224-400000000000-22004-400-22-2200000000000000000000000000000000000
χ764-4-444-20-404-4-422-24-202-220000-224-400000000000-2200-44002-22-200000000000000000000000000000000000
χ774-4-44-24040-422-4-44-2-202-220000-442-2000000000002-2000000000000000000i6−i6i6−i6−i6i6−i6i60000000000000000000
χ784-4-44-24040-422-4-44-2-202-220000-442-2000000000002-2000000000000000000−i6i6−i6i6i6−i6i6−i60000000000000000000
χ794-4-44-240-40422-4-44-2-202-2200004-4-2200000000000-220000000000000022−2222−22−22−22−22−220000000000000000000
χ804-4-44-240-40422-4-44-2-202-2200004-4-2200000000000-2200000000000000−2222−22222−22−22−22−20000000000000000000
χ8188-8-88-40000-88-444-8-4044-4000000000000000000000000000000000000000000000000000000000000000000
χ8288-8-8-4-400004-4-444420-2-2200000000−4i34i3000000000002i3−2i30000000000000000000000000000000000000000000
χ8388-8-8-4-400004-4-444420-2-22000000004i3−4i300000000000−2i32i30000000000000000000000000000000000000000000
χ848-88-8-4-480-80-444-444202-2-2-44-4400000000000002-200000000000000000000000000000000000000000000000
χ858-88-8-4-4-8080-444-444202-2-24-44-40000000000000-2200000000000000000000000000000000000000000000000
χ868-8-88-4-4080-84444-4-420-22-200004-44-400000000000-22000000000000000000000000000000000000000000000
χ878-8-88-4-40-8084444-4-420-22-20000-44-44000000000002-2000000000000000000000000000000000000000000000

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