Finite Group Databasebeta

← Group #10698909

Character table — Group #10698909

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order12222234444444466612121212446688888888121212121212121212122424242424242424242424242424242488882424242424242424444488884488
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
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1
χ92222222222-2-2-22-2222-2-2-2-2-2-222000000002222-2-2-2-2-2-2000000000000000000000000000000000000002i−2i
χ102222222222-2-2-22-2222-2-2-2-2-2-222000000002222-2-2-2-2-2-200000000000000000000000000000000000000−2i2i
χ112222222-2-2-2222-222222222-2-22200000000-2-2-2-222-2-2-2-2000000000000000000000000000022-2-200000000
χ122222222-2-2-2222-222222222-2-22200000000-2-2-2-222-2-2-2-20000000000000000000000000000-2-22200000000
χ132222222-2-2-2-2-2-2-2-2222-2-2-2-2222200000000-2-2-2-2-2-222220000000000000000002i−2i00002i2i−2i−2i000000000000
χ142222222-2-2-2-2-2-2-2-2222-2-2-2-2222200000000-2-2-2-2-2-22222000000000000000000−2i2i0000−2i−2i2i2i000000000000
χ15222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1000000000000
χ16222222-122222222-1-1-1-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111000000000000
χ17222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-11111000000000000
χ18222222-122222222-1-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-1000000000000
χ19222222-1-2-2-2-2-2-2-2-2-1-1-1111122-1-100000000111111-1-1-1-1−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3002i−2i33−3−3−i−iii000000000000
χ20222222-1-2-2-2-2-2-2-2-2-1-1-1111122-1-100000000111111-1-1-1-1−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i300−2i2i−3−333ii−i−i000000000000
χ21222222-1-2-2-2-2-2-2-2-2-1-1-1111122-1-100000000111111-1-1-1-1i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3002i−2i−3−333−i−iii000000000000
χ22222222-1-2-2-2-2-2-2-2-2-1-1-1111122-1-100000000111111-1-1-1-1i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i300−2i2i33−3−3ii−i−i000000000000
χ232222-2-2222-22-2-2-22222-2-2-2-22-2-2-20000000022-2-22222-2-2000000000000000000000000000000002i2i−2i−2i0000
χ242222-2-2222-22-2-2-22222-2-2-2-22-2-2-20000000022-2-22222-2-200000000000000000000000000000000−2i−2i2i2i0000
χ252222-2-2222-2-222-2-22222222-22-2-20000000022-2-2-2-2-2-22200000000000000002-2002-22-20000000000000000
χ262222-2-2222-2-222-2-22222222-22-2-20000000022-2-2-2-2-2-2220000000000000000-2200-22-220000000000000000
χ272222-2-22-2-222-2-222222-2-2-2-2-22-2-22222-2-2-2-2-2-22222-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ282222-2-22-2-222-2-222222-2-2-2-2-22-2-2-2-2-2-22222-2-22222-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ292222-2-22-2-22-2222-222222222-2-2-200000000-2-222-2-222-2-20000000000000000000000000000000000002-200
χ302222-2-22-2-22-2222-222222222-2-2-200000000-2-222-2-222-2-2000000000000000000000000000000000000-2200
χ312222-2-2-122-2-222-2-2-1-1-1-1-1-1-1-221100000000-1-1111111-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i32-200-11-11−i3i3−i3i3000000000000
χ322222-2-2-122-2-222-2-2-1-1-1-1-1-1-1-221100000000-1-1111111-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3-22001-11-1i3−i3i3−i3000000000000
χ332222-2-2-122-2-222-2-2-1-1-1-1-1-1-1-221100000000-1-1111111-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i32-200-11-11i3−i3i3−i3000000000000
χ342222-2-2-122-2-222-2-2-1-1-1-1-1-1-1-221100000000-1-1111111-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3-22001-11-1−i3i3−i3i3000000000000
χ352222-2-2-1-2-222-2-222-1-1-11111-22112222-2-2-2-211-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111100003−3−333−3−33000000000000
χ362222-2-2-1-2-222-2-222-1-1-11111-22112222-2-2-2-211-1-1-1-111-1-1-1-1-1-11111-1-1-1-111110000−333−3−333−3000000000000
χ372222-2-2-1-2-222-2-222-1-1-11111-2211-2-2-2-2222211-1-1-1-111-1-11111-1-1-1-11111-1-1-1-100003−3−33−333−3000000000000
χ382222-2-2-1-2-222-2-222-1-1-11111-2211-2-2-2-2222211-1-1-1-111-1-11111-1-1-1-11111-1-1-1-10000−333−33−3−33000000000000
χ3922-2-22-22000-22-2022-2-222-2-2002-2−i2−i2i2i2−i2−i2i2i200002-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000002i−2i2−22−20000
χ4022-2-22-22000-22-2022-2-222-2-2002-2−i2−i2i2i2−i2−i2i2i200002-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000000000−2i2i−22−220000
χ4122-2-22-22000-22-2022-2-222-2-2002-2i2i2−i2−i2i2i2−i2−i200002-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000002i−2i−22−220000
χ4222-2-22-22000-22-2022-2-222-2-2002-2i2i2−i2−i2i2i2−i2−i200002-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000000000−2i2i2−22−20000
χ4322-2-2-222000-2-22022-2-2-2-22200-22−i2−i2i2i2i2i2−i2−i200002-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000002-200−i2i2i2−i20000
χ4422-2-2-222000-2-22022-2-2-2-22200-22−i2−i2i2i2i2i2−i2−i200002-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000-2200i2−i2−i2i20000
χ4522-2-2-222000-2-22022-2-2-2-22200-22i2i2−i2−i2−i2−i2i2i200002-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000002-200i2−i2−i2i20000
χ4622-2-2-222000-2-22022-2-2-2-22200-22i2i2−i2−i2−i2−i2i2i200002-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000-2200−i2i2i2−i20000
χ47444444-2444-4-4-44-4-2-2-22222-4-4-2-200000000-2-2-2-22222220000000000000000000000000000000000000000
χ48444444-2-4-4-4444-44-2-2-2-2-2-2-2-4-4-2-2000000002222-2-222220000000000000000000000000000000000000000
χ494444-4-4-244-44-4-4-44-2-2-222224-42200000000-2-222-2-2-2-2220000000000000000000000000000000000000000
χ504444-4-4-2-4-44-4444-4-2-2-2-2-2-2-24-4220000000022-2-222-2-2220000000000000000000000000000000000000000
χ5144-4-44-440004-440-44-4-4-4-444004-4000000000000-4400000000000000000000000000000000000000000000
χ5244-4-44-4-20004-440-4-22222-2-200-220000000000002-2000066−6−666−6−6−6−666−6−666000000000000000000000000
χ5344-4-44-4-20004-440-4-22222-2-200-220000000000002-20000−6−666−6−66666−6−666−6−6000000000000000000000000
χ5444-4-44-4-2000-44-404-222-2-22200-22−2i2−2i22i22i2−2i2−2i22i22i20000-220000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ5544-4-44-4-2000-44-404-222-2-22200-222i22i2−2i2−2i22i22i2−2i2−2i20000-220000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ5644-4-4-44400044-40-44-4-444-4-400-44000000000000-4400000000000000000000000000000000000000000000
χ5744-4-4-44-200044-40-4-222-2-222002-20000000000002-2000066−6−6−6−666−6−66666−6−6000000000000000000000000
χ5844-4-4-44-200044-40-4-222-2-222002-20000000000002-20000−6−66666−6−666−6−6−6−666000000000000000000000000
χ5944-4-4-44-2000-4-4404-22222-2-2002-2−2i2−2i22i22i22i22i2−2i2−2i20000-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000000000000000
χ6044-4-4-44-2000-4-4404-22222-2-2002-22i22i2−2i2−2i2−2i2−2i22i22i20000-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000000000000000
χ614-44-4004004000-40-44-400000000000022−2222−22004-4000000000022−2222−22000022−2222−22000000000000000000000000
χ624-44-4004004000-40-44-4000000000000−2222−2222004-40000000000−2222−22220000−2222−2222000000000000000000000000
χ634-44-400400-400040-44-400000000−2i22i2−2i22i2000000-44000000−2i22i2−2i22i20000−2i22i2−2i22i20000000000000000000000000000
χ644-44-400400-400040-44-4000000002i2−2i22i2−2i2000000-440000002i2−2i22i2−2i200002i2−2i22i2−2i20000000000000000000000000000
χ654-44-400-2004000-402-2223−2323−230000000022−2222−2200-220023−23006−66−6−22−22−66−66−22−22000000000000000000000000
χ664-44-400-2004000-402-2223−2323−2300000000−2222−222200-220023−2300−66−662−22−26−66−62−22−2000000000000000000000000
χ674-44-400-2004000-402-22−2323−23230000000022−2222−2200-2200−232300−66−66−22−226−66−6−22−22000000000000000000000000
χ684-44-400-2004000-402-22−2323−232300000000−2222−222200-2200−2323006−66−62−22−2−66−662−22−2000000000000000000000000
χ694-44-400-200-4000402-2223−2323−230000−2i22i2−2i22i20000002-200−232300i2−i2i2−i2−i6i6−i6i6i2−i2i2−i2i6−i6i6−i6000000000000000000000000
χ704-44-400-200-4000402-2223−2323−2300002i2−2i22i2−2i20000002-200−232300−i2i2−i2i2i6−i6i6−i6−i2i2−i2i2−i6i6−i6i6000000000000000000000000
χ714-44-400-200-4000402-22−2323−23230000−2i22i2−2i22i20000002-20023−2300i2−i2i2−i2i6−i6i6−i6i2−i2i2−i2−i6i6−i6i6000000000000000000000000
χ724-44-400-200-4000402-22−2323−232300002i2−2i22i2−2i20000002-20023−2300−i2i2−i2i2−i6i6−i6i6−i2i2−i2i2i6−i6i6−i6000000000000000000000000
χ734-4-440044i−4i000000-4-44000000002-2-222i−2i−2i2i4i−4i000000002-2-222i−2i−2i2i2-2-222i−2i−2i2i000000000000000000000000
χ744-4-440044i−4i000000-4-4400000000-222-2−2i2i2i−2i4i−4i00000000-222-2−2i2i2i−2i-222-2−2i2i2i−2i000000000000000000000000
χ754-4-44004−4i4i000000-4-44000000002-2-22−2i2i2i−2i−4i4i000000002-2-22−2i2i2i−2i2-2-22−2i2i2i−2i000000000000000000000000
χ764-4-44004−4i4i000000-4-4400000000-222-22i−2i−2i2i−4i4i00000000-222-22i−2i−2i2i-222-22i−2i−2i2i000000000000000000000000
χ774-4-4400-24i−4i00000022-223−23−232300002-2-222i−2i−2i2i−2i2i000000−2i32i3−1+i31−i31−i3−1+i32ζ22−2ζ22−2ζ222ζ22−1−i31+i31+i3−1−i32ζ14−2ζ14−2ζ142ζ14000000000000000000000000
χ784-4-4400-24i−4i00000022-223−23−23230000-222-2−2i2i2i−2i−2i2i000000−2i32i31−i3−1+i3−1+i31−i3−2ζ222ζ222ζ22−2ζ221+i3−1−i3−1−i31+i3−2ζ142ζ142ζ14−2ζ14000000000000000000000000
χ794-4-4400-24i−4i00000022-2−232323−2300002-2-222i−2i−2i2i−2i2i0000002i3−2i3−1−i31+i31+i3−1−i32ζ14−2ζ14−2ζ142ζ14−1+i31−i31−i3−1+i32ζ22−2ζ22−2ζ222ζ22000000000000000000000000
χ804-4-4400-24i−4i00000022-2−232323−230000-222-2−2i2i2i−2i−2i2i0000002i3−2i31+i3−1−i3−1−i31+i3−2ζ142ζ142ζ14−2ζ141−i3−1+i3−1+i31−i3−2ζ222ζ222ζ22−2ζ22000000000000000000000000
χ814-4-4400-2−4i4i00000022-223−23−232300002-2-22−2i2i2i−2i2i−2i0000002i3−2i3−1−i31+i31+i3−1−i3−2ζ142ζ142ζ14−2ζ14−1+i31−i31−i3−1+i3−2ζ222ζ222ζ22−2ζ22000000000000000000000000
χ824-4-4400-2−4i4i00000022-223−23−23230000-222-22i−2i−2i2i2i−2i0000002i3−2i31+i3−1−i3−1−i31+i32ζ14−2ζ14−2ζ142ζ141−i3−1+i3−1+i31−i32ζ22−2ζ22−2ζ222ζ22000000000000000000000000
χ834-4-4400-2−4i4i00000022-2−232323−2300002-2-22−2i2i2i−2i2i−2i000000−2i32i3−1+i31−i31−i3−1+i3−2ζ222ζ222ζ22−2ζ22−1−i31+i31+i3−1−i3−2ζ142ζ142ζ14−2ζ14000000000000000000000000
χ844-4-4400-2−4i4i00000022-2−232323−230000-222-22i−2i−2i2i2i−2i000000−2i32i31−i3−1+i3−1+i31−i32ζ22−2ζ22−2ζ222ζ221+i3−1−i3−1−i31+i32ζ14−2ζ14−2ζ142ζ14000000000000000000000000

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