Finite Group Databasebeta

← Group #10696007

Character table — Group #10696007

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888888888888888816161616161624242424484848484848
order12222234444666121212124444661212121212124444888812121212121212121212242424242424242444121212122244448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-1
χ6111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ9222222222-2-222222222-2-2-22222-2-2-2-222-2-20000-2-22222-2-2-2-2000000000000000000000000
χ10222222222-2-222222222-2-2-22222-2-2-2-2-2-2220000-2-2-2-2-2-22222000000000000000000000000
χ112222222-2-222222-2-2-2-2-22-2-222-2-222-2-2000000002-2000000000000000000000000002-20000
χ122222222-2-222222-2-2-2-2-22-2-222-2-222-2-2000000002-200000000000000000000000000-220000
χ132222222-2-2-2-2222-2-2-2-2-2-22222-2-2-2-22200000000-22000000000000000000000022-2-2000000
χ142222222-2-2-2-2222-2-2-2-2-2-22222-2-2-2-22200000000-220000000000000000000000-2-222000000
χ15222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10000000000
χ16222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111-2-211110000000000
χ17222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1-2-211110000000000
χ18222222-12222-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111111111111122-1-1-1-10000000000
χ19222222-122-2-2-1-1-1-1-1-1-12-2-2-2-1-1-1-1111122-2-2000011-1-1-1-11111−i3−i3−i3−i3i3i3i3i300−i3−i3i3i30000000000
χ20222222-122-2-2-1-1-1-1-1-1-12-2-2-2-1-1-1-1111122-2-2000011-1-1-1-11111i3i3i3i3−i3−i3−i3−i300i3i3−i3−i30000000000
χ21222222-122-2-2-1-1-1-1-1-1-12-2-2-2-1-1-1-11111-2-2220000111111-1-1-1-1−i3−i3−i3−i3i3i3i3i300i3i3−i3−i30000000000
χ22222222-122-2-2-1-1-1-1-1-1-12-2-2-2-1-1-1-11111-2-2220000111111-1-1-1-1i3i3i3i3−i3−i3−i3−i300−i3−i3i3i30000000000
χ232222-2-2222222222222-2-22-2-2-2-2-2222200000000-2-200000000000000000000000000002-200
χ242222-2-2222222222222-2-22-2-2-2-2-2222200000000-2-20000000000000000000000000000-2200
χ252222-2-2222-2-22222222-22-22-2-2-2-2-2-2-2-200000000220000000000000000000000000000002-2
χ262222-2-2222-2-22222222-22-22-2-2-2-2-2-2-2-20000000022000000000000000000000000000000-22
χ272222-2-22-2-222222-2-2-2-22-2-22-2-22222-2-200000000-2200000000000000002-22-22-20000000000
χ282222-2-22-2-222222-2-2-2-22-2-22-2-22222-2-200000000-220000000000000000-22-22-220000000000
χ292222-2-22-2-2-2-2222-2-2-2-2222-2-2-222-2-22200002i2i−2i−2i2-2000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ302222-2-22-2-2-2-2222-2-2-2-2222-2-2-222-2-2220000−2i−2i2i2i2-200000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ312222-2-2-1-2-222-1-1-111112-2-2211-1-1-1-111000000001-133−3−333−3−333−3−3−3−3332-2-11-110000000000
χ322222-2-2-1-2-222-1-1-111112-2-2211-1-1-1-111000000001-133−3−333−3−3−3−33333−3−3-221-11-10000000000
χ332222-2-2-1-2-222-1-1-111112-2-2211-1-1-1-111000000001-1−3−333−3−33333−3−3−3−333-221-11-10000000000
χ342222-2-2-1-2-222-1-1-111112-2-2211-1-1-1-111000000001-1−3−333−3−333−3−33333−3−32-2-11-110000000000
χ352222-2-2-1-2-2-2-2-1-1-11111222-211-1-111-1-100002i2i−2i−2i-1133−3−3−3−333−i−iii−i−iii00−i3i3i3−i30000000000
χ362222-2-2-1-2-2-2-2-1-1-11111222-211-1-111-1-100002i2i−2i−2i-11−3−33333−3−3−i−iii−i−iii00i3−i3−i3i30000000000
χ372222-2-2-1-2-2-2-2-1-1-11111222-211-1-111-1-10000−2i−2i2i2i-1133−3−3−3−333ii−i−iii−i−i00i3−i3−i3i30000000000
χ382222-2-2-1-2-2-2-2-1-1-11111222-211-1-111-1-10000−2i−2i2i2i-11−3−33333−3−3ii−i−iii−i−i00−i3i3i3−i30000000000
χ39444444-2-4-444-2-2-22222-44-4-4-2-222-2-22200000000-2200000000000000000000000000000000
χ40444444-2-4-4-4-4-2-2-22222-4-444-2-22222-2-2000000002-200000000000000000000000000000000
χ414444-4-4-24444-2-2-2-2-2-2-2-4-44-42222-2-2-2-2000000002200000000000000000000000000000000
χ424444-4-4-244-4-4-2-2-2-2-2-2-2-44-442222222200000000-2-200000000000000000000000000000000
χ4344-4-44-4400004-4-4000000004-400000000002-22-200000000002-22-22-22-20000000000000000
χ4444-4-44-4400004-4-4000000004-40000000000-22-220000000000-22-22-22-220000000000000000
χ4544-4-44-4-20000-222−2i3−2i32i32i30000-22−2i32i3000000002-22-20000000000−1−i31+i3−1−i31+i3−1+i31−i3−1+i31−i30000000000000000
χ4644-4-44-4-20000-222−2i3−2i32i32i30000-22−2i32i300000000-22-2200000000001+i3−1−i31+i3−1−i31−i3−1+i31−i3−1+i30000000000000000
χ4744-4-44-4-20000-2222i32i3−2i3−2i30000-222i3−2i3000000002-22-20000000000−1+i31−i3−1+i31−i3−1−i31+i3−1−i31+i30000000000000000
χ4844-4-44-4-20000-2222i32i3−2i3−2i30000-222i3−2i300000000-22-2200000000001−i3−1+i31−i3−1+i31+i3−1−i31+i3−1−i30000000000000000
χ4944-4-4-44400004-4-400000000-4400000000002i−2i−2i2i00000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ5044-4-4-44400004-4-400000000-440000000000−2i2i2i−2i0000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ5144-4-4-44-20000-222−2i3−2i32i32i300002-22i3−2i3000000002i−2i−2i2i00000000002ζ7−2ζ7−2ζ72ζ72ζ11−2ζ11−2ζ112ζ110000000000000000
χ5244-4-4-44-20000-222−2i3−2i32i32i300002-22i3−2i300000000−2i2i2i−2i0000000000−2ζ72ζ72ζ7−2ζ7−2ζ112ζ112ζ11−2ζ110000000000000000
χ5344-4-4-44-20000-2222i32i3−2i3−2i300002-2−2i32i3000000002i−2i−2i2i00000000002ζ11−2ζ11−2ζ112ζ112ζ7−2ζ7−2ζ72ζ70000000000000000
χ5444-4-4-44-20000-2222i32i3−2i3−2i300002-2−2i32i300000000−2i2i2i−2i0000000000−2ζ112ζ112ζ11−2ζ11−2ζ72ζ72ζ7−2ζ70000000000000000
χ554-44-4004004-4-44-40000000000004-4002i−2i2i−2i0000002i−2i2i−2i2i−2i2i−2i000000000000000000000000
χ564-44-4004004-4-44-40000000000004-400−2i2i−2i2i000000−2i2i−2i2i−2i2i−2i2i000000000000000000000000
χ574-44-400400-44-44-4000000000000-44002i−2i−2i2i0000002i−2i2i−2i−2i2i−2i2i000000000000000000000000
χ584-44-400400-44-44-4000000000000-4400−2i2i2i−2i000000−2i2i−2i2i2i−2i2i−2i000000000000000000000000
χ594-44-400-2004-42-2223−2323−2300000000-2223−232i−2i2i−2i000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000000000000000000000000
χ604-44-400-2004-42-2223−2323−2300000000-2223−23−2i2i−2i2i000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000000000000000000000000
χ614-44-400-2004-42-22−2323−232300000000-22−23232i−2i2i−2i000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000000000000000000000000
χ624-44-400-2004-42-22−2323−232300000000-22−2323−2i2i−2i2i000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000000000000000000000000
χ634-44-400-200-442-2223−2323−23000000002-2−23232i−2i−2i2i000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000000000000000000000000
χ644-44-400-200-442-2223−2323−23000000002-2−2323−2i2i2i−2i000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000000000000000000000000
χ654-44-400-200-442-22−2323−2323000000002-223−232i−2i−2i2i000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000000000000000000000000
χ664-44-400-200-442-22−2323−2323000000002-223−23−2i2i2i−2i000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000000000000000000000000
χ674-4-440044i−4i00-4-444i−4i−4i4i000000000000000000000000000000000000000000002-22i−2i000000
χ684-4-440044i−4i00-4-444i−4i−4i4i00000000000000000000000000000000000000000000-22−2i2i000000
χ694-4-44004−4i4i00-4-44−4i4i4i−4i000000000000000000000000000000000000000000002-2−2i2i000000
χ704-4-44004−4i4i00-4-44−4i4i4i−4i00000000000000000000000000000000000000000000-222i−2i000000
χ718-8-8800-48i−8i0044-4−4i4i4i−4i000000000000000000000000000000000000000000000000000000
χ728-8-8800-4−8i8i0044-44i−4i−4i4i000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.