Finite Group Databasebeta

← Group #10696946

Character table — Group #10696946

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order12222234444444466666664488888888121212121212121212121212242424242424242424242424242424242244666612121212888888882488
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
χ9222222222-2-2-2-2-2-222222222-200000000-2-2-2-2-2-22222-2-2000000000000000000000000000000000000002i−2i
χ10222222222-2-2-2-2-2-222222222-200000000-2-2-2-2-2-22222-2-200000000000000000000000000000000000000−2i2i
χ112222222-2-22-2-22222222222-2-2000000002222-2-2-2-2-2-2-2-2000000000000000000000000000022-2-200000000
χ122222222-2-22-2-22222222222-2-2000000002222-2-2-2-2-2-2-2-20000000000000000000000000000-2-22200000000
χ132222222-2-2-222-2-2-22222222-2200000000-2-2-2-222-2-2-2-2220000000000000000002-2000022-2-2000000000000
χ142222222-2-2-222-2-2-22222222-2200000000-2-2-2-222-2-2-2-222000000000000000000-220000-2-222000000000000
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
χ19222222-1-2-2-222-2-2-2-1-1-1-1-1-1-1-22000000001111-1-11111-1-1−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3002-2−i3−i3i3i3-1-111000000000000
χ20222222-1-2-2-222-2-2-2-1-1-1-1-1-1-1-22000000001111-1-11111-1-1−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i300-22i3i3−i3−i311-1-1000000000000
χ21222222-1-2-2-222-2-2-2-1-1-1-1-1-1-1-22000000001111-1-11111-1-1i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3002-2i3i3−i3−i3-1-111000000000000
χ22222222-1-2-2-222-2-2-2-1-1-1-1-1-1-1-22000000001111-1-11111-1-1i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i300-22−i3−i3i3i311-1-1000000000000
χ232222-2-22222-2-2-2-22-2-2-2-2222-222222-2-2-2-222-2-2-2-222-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ242222-2-22222-2-2-2-22-2-2-2-2222-22-2-2-2-2222222-2-2-2-222-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ252222-2-2222-22222-2-2-2-2-2222-2-200000000-2-2222222-2-2-2-20000000000000000000000000000000000002-200
χ262222-2-2222-22222-2-2-2-2-2222-2-200000000-2-2222222-2-2-2-2000000000000000000000000000000000000-2200
χ272222-2-22-2-2222-2-22-2-2-2-22222-20000000022-2-222-2-222-2-20000000000000000000000000000000022-2-20000
χ282222-2-22-2-2222-2-22-2-2-2-22222-20000000022-2-222-2-222-2-200000000000000000000000000000000-2-2220000
χ292222-2-22-2-2-2-2-222-2-2-2-2-22222200000000-2-222-2-2-2-2222200000000000000002-2002-22-20000000000000000
χ302222-2-22-2-2-2-2-222-2-2-2-2-22222200000000-2-222-2-2-2-222220000000000000000-2200-22-220000000000000000
χ312222-2-2-1222-2-2-2-221111-1-1-1-222222-2-2-2-2-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111110000−i3i3i3−i3−i3i3−i3i3000000000000
χ322222-2-2-1222-2-2-2-221111-1-1-1-222222-2-2-2-2-1-11111-1-111-1-1-1-1-1-11111-1-1-1-111110000i3−i3−i3i3i3−i3i3−i3000000000000
χ332222-2-2-1222-2-2-2-221111-1-1-1-22-2-2-2-22222-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-10000−i3i3i3−i3i3−i3i3−i3000000000000
χ342222-2-2-1222-2-2-2-221111-1-1-1-22-2-2-2-22222-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-10000i3−i3−i3i3−i3i3−i3i3000000000000
χ352222-2-2-1-2-2-2-2-222-21111-1-1-1220000000011-1-11111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i32-200-11-11−i3i3i3−i3000000000000
χ362222-2-2-1-2-2-2-2-222-21111-1-1-1220000000011-1-11111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3-22001-11-1i3−i3−i3i3000000000000
χ372222-2-2-1-2-2-2-2-222-21111-1-1-1220000000011-1-11111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i32-200-11-11i3−i3−i3i3000000000000
χ382222-2-2-1-2-2-2-2-222-21111-1-1-1220000000011-1-11111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3-22001-11-1−i3i3i3−i3000000000000
χ392-2-222-22002002-2-222-2-22-2-200−i2−i2i2i2−i2−i2i2i22-22-200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000002-2−i2i2−i2i20000
χ402-2-222-22002002-2-222-2-22-2-200−i2−i2i2i2−i2−i2i2i22-22-200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000-22i2−i2i2−i20000
χ412-2-222-22002002-2-222-2-22-2-200i2i2−i2−i2i2i2−i2−i22-22-200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000002-2i2−i2i2−i20000
χ422-2-222-22002002-2-222-2-22-2-200i2i2−i2−i2i2i2−i2−i22-22-200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000-22−i2i2−i2i20000
χ432-2-22-22200200-22-2-2-2222-2-200−i2−i2i2i2i2i2−i2−i22-2-2200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000002-200−i2i2i2−i20000
χ442-2-22-22200200-22-2-2-2222-2-200−i2−i2i2i2i2i2−i2−i22-2-2200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000-2200i2−i2−i2i20000
χ452-2-22-22200200-22-2-2-2222-2-200i2i2−i2−i2−i2−i2i2i22-2-2200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000002-200i2−i2−i2i20000
χ462-2-22-22200200-22-2-2-2222-2-200i2i2−i2−i2−i2−i2i2i22-2-2200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000-2200−i2i2i2−i20000
χ47444444-244-4-4-4-4-4-4-2-2-2-2-2-2-24-400000000222222-2-2-2-2220000000000000000000000000000000000000000
χ48444444-2-4-44-4-4444-2-2-2-2-2-2-2-4-400000000-2-2-2-2222222220000000000000000000000000000000000000000
χ494444-4-4-244-44444-42222-2-2-2-4-40000000022-2-2-2-2-2-222220000000000000000000000000000000000000000
χ504444-4-4-2-4-4444-4-442222-2-2-24-400000000-2-222-2-222-2-2220000000000000000000000000000000000000000
χ5144-4-40040004-40000000-44-4002i−2i2i−2i2i−2i2i−2i00004-40000002i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ5244-4-40040004-40000000-44-400−2i2i−2i2i−2i2i−2i2i00004-4000000−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ5344-4-4004000-440000000-44-4002i−2i2i−2i−2i2i−2i2i0000-440000002i−2i2i−2i−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ5444-4-4004000-440000000-44-400−2i2i−2i2i2i−2i2i−2i0000-44000000−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ5544-4-400-20004-4000−2i32i3−2i32i32-22002i−2i2i−2i2i−2i2i−2i0000-220000−2i32i32ζ14−2ζ142ζ14−2ζ142ζ14−2ζ142ζ14−2ζ142ζ22−2ζ222ζ22−2ζ222ζ22−2ζ222ζ22−2ζ22000000000000000000000000
χ5644-4-400-20004-4000−2i32i3−2i32i32-2200−2i2i−2i2i−2i2i−2i2i0000-220000−2i32i3−2ζ142ζ14−2ζ142ζ14−2ζ142ζ14−2ζ142ζ14−2ζ222ζ22−2ζ222ζ22−2ζ222ζ22−2ζ222ζ22000000000000000000000000
χ5744-4-400-20004-40002i3−2i32i3−2i32-22002i−2i2i−2i2i−2i2i−2i0000-2200002i3−2i32ζ22−2ζ222ζ22−2ζ222ζ22−2ζ222ζ22−2ζ222ζ14−2ζ142ζ14−2ζ142ζ14−2ζ142ζ14−2ζ14000000000000000000000000
χ5844-4-400-20004-40002i3−2i32i3−2i32-2200−2i2i−2i2i−2i2i−2i2i0000-2200002i3−2i3−2ζ222ζ22−2ζ222ζ22−2ζ222ζ22−2ζ222ζ22−2ζ142ζ14−2ζ142ζ14−2ζ142ζ14−2ζ142ζ14000000000000000000000000
χ5944-4-400-2000-44000−2i32i3−2i32i32-22002i−2i2i−2i−2i2i−2i2i00002-200002i3−2i32ζ22−2ζ222ζ22−2ζ22−2ζ222ζ22−2ζ222ζ222ζ14−2ζ142ζ14−2ζ14−2ζ142ζ14−2ζ142ζ14000000000000000000000000
χ6044-4-400-2000-44000−2i32i3−2i32i32-2200−2i2i−2i2i2i−2i2i−2i00002-200002i3−2i3−2ζ222ζ22−2ζ222ζ222ζ22−2ζ222ζ22−2ζ22−2ζ142ζ14−2ζ142ζ142ζ14−2ζ142ζ14−2ζ14000000000000000000000000
χ6144-4-400-2000-440002i3−2i32i3−2i32-22002i−2i2i−2i−2i2i−2i2i00002-20000−2i32i32ζ14−2ζ142ζ14−2ζ14−2ζ142ζ14−2ζ142ζ142ζ22−2ζ222ζ22−2ζ22−2ζ222ζ22−2ζ222ζ22000000000000000000000000
χ6244-4-400-2000-440002i3−2i32i3−2i32-2200−2i2i−2i2i2i−2i2i−2i00002-20000−2i32i3−2ζ142ζ14−2ζ142ζ142ζ14−2ζ142ζ14−2ζ14−2ζ222ζ22−2ζ222ζ222ζ22−2ζ222ζ22−2ζ22000000000000000000000000
χ634-44-40044-40000000000-4-4400000022−22−22220000004-40000000022−22−2222000022−22−2222000000000000000000000000
χ644-44-40044-40000000000-4-44000000−222222−220000004-400000000−222222−220000−222222−22000000000000000000000000
χ654-44-4004-440000000000-4-440022−22−22220000000000-44000022−22−2222000022−22−22220000000000000000000000000000
χ664-44-4004-440000000000-4-4400−222222−220000000000-440000−222222−220000−222222−220000000000000000000000000000
χ674-44-400-24-4000000−2i32i32i3−2i322-200000022−22−2222000000-22−2i32i300i6−i6−i6i6−222−2−i6i6i6−i6−222−2000000000000000000000000
χ684-44-400-24-4000000−2i32i32i3−2i322-2000000−222222−22000000-22−2i32i300−i6i6i6−i62−2−22i6−i6−i6i62−2−22000000000000000000000000
χ694-44-400-24-40000002i3−2i3−2i32i322-200000022−22−2222000000-222i3−2i300−i6i6i6−i6−222−2i6−i6−i6i6−222−2000000000000000000000000
χ704-44-400-24-40000002i3−2i3−2i32i322-2000000−222222−22000000-222i3−2i300i6−i6−i6i62−2−22−i6i6i6−i62−2−22000000000000000000000000
χ714-44-400-2-44000000−2i32i32i3−2i322-20022−22−222200000000002-22i3−2i300−222−2i6−i6−i6i6−222−2−i6i6i6−i6000000000000000000000000
χ724-44-400-2-44000000−2i32i32i3−2i322-200−222222−2200000000002-22i3−2i3002−2−22−i6i6i6−i62−2−22i6−i6−i6i6000000000000000000000000
χ734-44-400-2-440000002i3−2i3−2i32i322-20022−22−222200000000002-2−2i32i300−222−2−i6i6i6−i6−222−2i6−i6−i6i6000000000000000000000000
χ744-44-400-2-440000002i3−2i3−2i32i322-200−222222−2200000000002-2−2i32i3002−2−22i6−i6−i6i62−2−22−i6i6i6−i6000000000000000000000000
χ754-4-444-4400-400-44444-4-44-4-40000000000-44-44000000000000000000000000000000000000000000000000
χ764-4-444-4-2004004-4-4-2-222-22200−2i2−2i22i22i2−2i2−2i22i22i2-22-2200000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ774-4-444-4-2004004-4-4-2-222-222002i22i2−2i2−2i22i22i2−2i2−2i2-22-2200000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ784-4-444-4-200-400-444-2-222-22200000000002-22-20000000066−6−666−6−6−6−666−6−666000000000000000000000000
χ794-4-444-4-200-400-444-2-222-22200000000002-22-200000000−6−666−6−66666−6−666−6−6000000000000000000000000
χ804-4-44-44400-4004-44-4-4444-4-40000000000-444-4000000000000000000000000000000000000000000000000
χ814-4-44-44-200400-44-422-2-2-22200−2i2−2i22i22i22i22i2−2i2−2i2-222-200000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000
χ824-4-44-44-200400-44-422-2-2-222002i22i2−2i2−2i2−2i2−2i22i22i2-222-200000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ834-4-44-44-200-4004-4422-2-2-22200000000002-2-220000000066−6−6−6−666−6−66666−6−6000000000000000000000000
χ844-4-44-44-200-4004-4422-2-2-22200000000002-2-2200000000−6−66666−6−666−6−6−6−666000000000000000000000000

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