Finite Group Databasebeta

← Group #10697002

Character table — Group #10697002

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order122222344444444666666644888888881212121212121212121212122424242424242424242424242424242444441212121212121212888888882488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ9222222222-2-2-2-2-2-222222222-200000000-2-2-2-22222-2-2-2-2000000000000000000000000000000000000002i−2i
χ10222222222-2-2-2-2-2-222222222-200000000-2-2-2-22222-2-2-2-200000000000000000000000000000000000000−2i2i
χ112222222-2-22-2-22222222222-2-2000000002222-2-2-2-2-2-2-2-20000000000000000000000000000000022-2-20000
χ122222222-2-22-2-22222222222-2-2000000002222-2-2-2-2-2-2-2-200000000000000000000000000000000-2-2220000
χ132222222-2-2-222-2-2-22222222-2200000000-2-2-2-2-2-2-2-2222200000000000000002-20022-2-20000000000000000
χ142222222-2-2-222-2-2-22222222-2200000000-2-2-2-2-2-2-2-222220000000000000000-2200-2-2220000000000000000
χ15222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ16222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ17222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-11111000000000000
χ18222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-1000000000000
χ19222222-1-2-2-222-2-2-2-1-1-1-1-1-1-1-220000000011111111-1-1-1-1−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i32-200-1-111−i3−i3i3i3000000000000
χ20222222-1-2-2-222-2-2-2-1-1-1-1-1-1-1-220000000011111111-1-1-1-1−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3-220011-1-1i3i3−i3−i3000000000000
χ21222222-1-2-2-222-2-2-2-1-1-1-1-1-1-1-220000000011111111-1-1-1-1i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i32-200-1-111i3i3−i3−i3000000000000
χ22222222-1-2-2-222-2-2-2-1-1-1-1-1-1-1-220000000011111111-1-1-1-1i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3-220011-1-1−i3−i3i3i3000000000000
χ232222-2-22222-2-2-2-22-2-2-2-2222-222222-2-2-2-222-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ242222-2-22222-2-2-2-22-2-2-2-2222-22-2-2-2-2222222-2-222-2-2-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ252222-2-2222-22222-2-2-2-2-2222-2-200000000-2-22222-2-222-2-20000000000000000000000000000000000002-200
χ262222-2-2222-22222-2-2-2-2-2222-2-200000000-2-22222-2-222-2-2000000000000000000000000000000000000-2200
χ272222-2-22-2-2222-2-22-2-2-2-22222-20000000022-2-2-2-22222-2-2000000000000000000000000000022-2-200000000
χ282222-2-22-2-2222-2-22-2-2-2-22222-20000000022-2-2-2-22222-2-20000000000000000000000000000-2-22200000000
χ292222-2-22-2-2-2-2-222-2-2-2-2-22222200000000-2-222-2-222-2-2220000000000000000002-200002-22-2000000000000
χ302222-2-22-2-2-2-2-222-2-2-2-2-22222200000000-2-222-2-222-2-222000000000000000000-220000-22-22000000000000
χ312222-2-2-1222-2-2-2-221111-1-1-1-222222-2-2-2-2-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111110000−i3i3−i3i3−i3i3i3−i3000000000000
χ322222-2-2-1222-2-2-2-221111-1-1-1-222222-2-2-2-2-1-111-1-11111-1-1-1-1-1-11111-1-1-1-111110000i3−i3i3−i3i3−i3−i3i3000000000000
χ332222-2-2-1222-2-2-2-221111-1-1-1-22-2-2-2-22222-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-10000−i3i3−i3i3i3−i3−i3i3000000000000
χ342222-2-2-1222-2-2-2-221111-1-1-1-22-2-2-2-22222-1-111-1-11111-1-11111-1-1-1-11111-1-1-1-10000i3−i3i3−i3−i3i3i3−i3000000000000
χ352222-2-2-1-2-2-2-2-222-21111-1-1-1220000000011-1-111-1-111-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3002-2−i3i3i3−i3-11-11000000000000
χ362222-2-2-1-2-2-2-2-222-21111-1-1-1220000000011-1-111-1-111-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i300-22i3−i3−i3i31-11-1000000000000
χ372222-2-2-1-2-2-2-2-222-21111-1-1-1220000000011-1-111-1-111-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3002-2i3−i3−i3i3-11-11000000000000
χ382222-2-2-1-2-2-2-2-222-21111-1-1-1220000000011-1-111-1-111-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i300-22−i3i3i3−i31-11-1000000000000
χ392-2-222-2200-2002-2222-2-22-2-20022−2−222−2−22-22-20000000022−2−222−2−222−2−222−2−2000000000000−i2i2−i2i2002i−2i0000
χ402-2-222-2200-2002-2222-2-22-2-20022−2−222−2−22-22-20000000022−2−222−2−222−2−222−2−2000000000000i2−i2i2−i200−2i2i0000
χ412-2-222-2200-2002-2222-2-22-2-200−2−222−2−2222-22-200000000−2−222−2−222−2−222−2−222000000000000−i2i2−i2i200−2i2i0000
χ422-2-222-2200-2002-2222-2-22-2-200−2−222−2−2222-22-200000000−2−222−2−222−2−222−2−222000000000000i2−i2i2−i2002i−2i0000
χ432-2-22-22200-200-222-2-2222-2-20022−2−2−2−2222-2-220000000022−2−2−2−22222−2−2−2−222000000000000−i2i2i2−i22i−2i000000
χ442-2-22-22200-200-222-2-2222-2-20022−2−2−2−2222-2-220000000022−2−2−2−22222−2−2−2−222000000000000i2−i2−i2i2−2i2i000000
χ452-2-22-22200-200-222-2-2222-2-200−2−22222−2−22-2-2200000000−2−22222−2−2−2−22222−2−2000000000000−i2i2i2−i2−2i2i000000
χ462-2-22-22200-200-222-2-2222-2-200−2−22222−2−22-2-2200000000−2−22222−2−2−2−22222−2−2000000000000i2−i2−i2i22i−2i000000
χ47444444-244-4-4-4-4-4-4-2-2-2-2-2-2-24-4000000002222-2-2-2-222220000000000000000000000000000000000000000
χ48444444-2-4-44-4-4444-2-2-2-2-2-2-2-4-400000000-2-2-2-2222222220000000000000000000000000000000000000000
χ494444-4-4-244-44444-42222-2-2-2-4-40000000022-2-2-2-222-2-2220000000000000000000000000000000000000000
χ504444-4-4-2-4-4444-4-442222-2-2-24-400000000-2-22222-2-2-2-2220000000000000000000000000000000000000000
χ5144-4-40040004-40000000-44-4002i−2i2i−2i2i−2i2i−2i000000004-4002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ5244-4-40040004-40000000-44-400−2i2i−2i2i−2i2i−2i2i000000004-400−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ5344-4-4004000-440000000-44-4002i−2i2i−2i−2i2i−2i2i00000000-44002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ5444-4-4004000-440000000-44-400−2i2i−2i2i2i−2i2i−2i00000000-4400−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ5544-4-400-20004-4000−2i32i3−2i32i32-22002i−2i2i−2i2i−2i2i−2i00000000-22−2i32i32ζ14−2ζ142ζ14−2ζ142ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ222ζ22−2ζ222ζ22−2ζ22000000000000000000000000
χ5644-4-400-20004-4000−2i32i3−2i32i32-2200−2i2i−2i2i−2i2i−2i2i00000000-22−2i32i3−2ζ142ζ14−2ζ142ζ14−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22−2ζ222ζ22−2ζ222ζ22000000000000000000000000
χ5744-4-400-20004-40002i3−2i32i3−2i32-22002i−2i2i−2i2i−2i2i−2i00000000-222i3−2i32ζ22−2ζ222ζ22−2ζ222ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ142ζ14−2ζ142ζ14−2ζ14000000000000000000000000
χ5844-4-400-20004-40002i3−2i32i3−2i32-2200−2i2i−2i2i−2i2i−2i2i00000000-222i3−2i3−2ζ222ζ22−2ζ222ζ22−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14−2ζ142ζ14−2ζ142ζ14000000000000000000000000
χ5944-4-400-2000-44000−2i32i3−2i32i32-22002i−2i2i−2i−2i2i−2i2i000000002-22i3−2i32ζ22−2ζ222ζ22−2ζ22−2ζ222ζ22−2ζ222ζ222ζ14−2ζ142ζ14−2ζ14−2ζ142ζ14−2ζ142ζ14000000000000000000000000
χ6044-4-400-2000-44000−2i32i3−2i32i32-2200−2i2i−2i2i2i−2i2i−2i000000002-22i3−2i3−2ζ222ζ22−2ζ222ζ222ζ22−2ζ222ζ22−2ζ22−2ζ142ζ14−2ζ142ζ142ζ14−2ζ142ζ14−2ζ14000000000000000000000000
χ6144-4-400-2000-440002i3−2i32i3−2i32-22002i−2i2i−2i−2i2i−2i2i000000002-2−2i32i32ζ14−2ζ142ζ14−2ζ14−2ζ142ζ14−2ζ142ζ142ζ22−2ζ222ζ22−2ζ22−2ζ222ζ22−2ζ222ζ22000000000000000000000000
χ6244-4-400-2000-440002i3−2i32i3−2i32-2200−2i2i−2i2i2i−2i2i−2i000000002-2−2i32i3−2ζ142ζ14−2ζ142ζ142ζ14−2ζ142ζ14−2ζ14−2ζ222ζ22−2ζ222ζ222ζ22−2ζ222ζ22−2ζ22000000000000000000000000
χ634-44-40044-40000000000-4-44000000−2i22i22i2−2i200004-40000000000−2i22i22i2−2i20000−2i22i22i2−2i2000000000000000000000000
χ644-44-40044-40000000000-4-440000002i2−2i2−2i22i200004-400000000002i2−2i2−2i22i200002i2−2i2−2i22i2000000000000000000000000
χ654-44-4004-440000000000-4-4400−2i22i22i2−2i200000000-44000000−2i22i22i2−2i20000−2i22i22i2−2i20000000000000000000000000000
χ664-44-4004-440000000000-4-44002i2−2i2−2i22i200000000-440000002i2−2i2−2i22i200002i2−2i2−2i22i20000000000000000000000000000
χ674-44-400-24-4000000−2i32i32i3−2i322-2000000−2i22i22i2−2i20000-22−2i32i300006−6−66i2−i2−i2i2−666−6i2−i2−i2i2000000000000000000000000
χ684-44-400-24-4000000−2i32i32i3−2i322-20000002i2−2i2−2i22i20000-22−2i32i30000−666−6−i2i2i2−i26−6−66−i2i2i2−i2000000000000000000000000
χ694-44-400-24-40000002i3−2i3−2i32i322-2000000−2i22i22i2−2i20000-222i3−2i30000−666−6i2−i2−i2i26−6−66i2−i2−i2i2000000000000000000000000
χ704-44-400-24-40000002i3−2i3−2i32i322-20000002i2−2i2−2i22i20000-222i3−2i300006−6−66−i2i2i2−i2−666−6−i2i2i2−i2000000000000000000000000
χ714-44-400-2-44000000−2i32i32i3−2i322-200−2i22i22i2−2i2000000002-22i3−2i30000i2−i2−i2i26−6−66i2−i2−i2i2−666−6000000000000000000000000
χ724-44-400-2-44000000−2i32i32i3−2i322-2002i2−2i2−2i22i2000000002-22i3−2i30000−i2i2i2−i2−666−6−i2i2i2−i26−6−66000000000000000000000000
χ734-44-400-2-440000002i3−2i3−2i32i322-200−2i22i22i2−2i2000000002-2−2i32i30000i2−i2−i2i2−666−6i2−i2−i2i26−6−66000000000000000000000000
χ744-44-400-2-440000002i3−2i3−2i32i322-2002i2−2i2−2i22i2000000002-2−2i32i30000−i2i2i2−i26−6−66−i2i2i2−i2−666−6000000000000000000000000
χ754-4-444-4400400-44-444-4-44-4-40000000000-44-44000000000000000000000000000000000000000000000000
χ764-4-444-4-200400-44-4-2-222-22200000000002-22-200000000i6i6−i6−i6i6i6−i6−i6−i6−i6i6i6−i6−i6i6i6000000000000000000000000
χ774-4-444-4-200400-44-4-2-222-22200000000002-22-200000000−i6−i6i6i6−i6−i6i6i6i6i6−i6−i6i6i6−i6−i6000000000000000000000000
χ784-4-444-4-200-4004-44-2-222-222002222−22−222222−22−22-22-2200000000−2−222−2−222−2−222−2−222000000000000000000000000
χ794-4-444-4-200-4004-44-2-222-22200−22−222222−22−222222-22-220000000022−2−222−2−222−2−222−2−2000000000000000000000000
χ804-4-44-444004004-4-4-4-4444-4-40000000000-444-4000000000000000000000000000000000000000000000000
χ814-4-44-44-2004004-4-422-2-2-22200000000002-2-2200000000i6i6−i6−i6−i6−i6i6i6−i6−i6i6i6i6i6−i6−i6000000000000000000000000
χ824-4-44-44-2004004-4-422-2-2-22200000000002-2-2200000000−i6−i6i6i6i6i6−i6−i6i6i6−i6−i6−i6−i6i6i6000000000000000000000000
χ834-4-44-44-200-400-44422-2-2-222002222−22−22−22−222222-222-200000000−2−22222−2−2−2−22222−2−2000000000000000000000000
χ844-4-44-44-200-400-44422-2-2-22200−22−2222222222−22−22-222-20000000022−2−2−2−22222−2−2−2−222000000000000000000000000

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