Finite Group Databasebeta

← Group #10698902

Character table — Group #10698902

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222222222222222244444444444444444444444444444444444444161616161616161616161616242424242424242448484848
order12222234444444466612121212446688888888121212121212121212122424242424242424242424242424242488882424242424242424224488884488
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
χ9222222222-2-2-222-22222222-2-2220000000022-2-2-2-2-2-2-2-2000000000000000000000000000022-2-200000000
χ10222222222-2-2-222-22222222-2-2220000000022-2-2-2-2-2-2-2-20000000000000000000000000000-2-22200000000
χ112222222-2-2222-2-22222-2-2-2-2-2-22200000000-2-22222-2-2-2-2000000000000000000000000000000000000002i−2i
χ122222222-2-2222-2-22222-2-2-2-2-2-22200000000-2-22222-2-2-2-200000000000000000000000000000000000000−2i2i
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
χ232222-2-222-222-22-2-22222222-22-2-200000000-2-222-2-2-2-22200000000000000002-2002-22-20000000000000000
χ242222-2-222-222-22-2-22222222-22-2-200000000-2-222-2-2-2-2220000000000000000-2200-22-220000000000000000
χ252222-2-222-2-2-222-2222222222-2-2-200000000-2-2-2-22222-2-20000000000000000000000000000000000002-200
χ262222-2-222-2-2-222-2222222222-2-2-200000000-2-2-2-22222-2-2000000000000000000000000000000000000-2200
χ272222-2-22-2222-2-22-2222-2-2-2-22-2-2-2000000002222-2-222-2-2000000000000000000000000000000002i2i−2i−2i0000
χ282222-2-22-2222-2-22-2222-2-2-2-22-2-2-2000000002222-2-222-2-200000000000000000000000000000000−2i−2i2i2i0000
χ292222-2-22-22-2-22-222222-2-2-2-2-22-2-22222-2-2-2-222-2-222-2-2222222-2-2-2-22222-2-2-2-2000000000000000000000000
χ302222-2-22-22-2-22-222222-2-2-2-2-22-2-2-2-2-2-2222222-2-222-2-222-2-2-2-22222-2-2-2-22222000000000000000000000000
χ312222-2-2-12-222-22-2-2-1-1-1-1-1-1-1-22110000000011-1-11111-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i32-200-11-11−i3i3−i3i3000000000000
χ322222-2-2-12-222-22-2-2-1-1-1-1-1-1-1-22110000000011-1-11111-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3-22001-11-1i3−i3i3−i3000000000000
χ332222-2-2-12-222-22-2-2-1-1-1-1-1-1-1-22110000000011-1-11111-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i32-200-11-11i3−i3i3−i3000000000000
χ342222-2-2-12-222-22-2-2-1-1-1-1-1-1-1-22110000000011-1-11111-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3-22001-11-1−i3i3−i3i3000000000000
χ352222-2-2-1-22-2-22-222-1-1-11111-22112222-2-2-2-2-1-111-1-111-1-1-1-1-1-11111-1-1-1-1111100003−3−333−3−33000000000000
χ362222-2-2-1-22-2-22-222-1-1-11111-22112222-2-2-2-2-1-111-1-111-1-1-1-1-1-11111-1-1-1-111110000−333−3−333−3000000000000
χ372222-2-2-1-22-2-22-222-1-1-11111-2211-2-2-2-22222-1-111-1-111-1-11111-1-1-1-11111-1-1-1-100003−3−33−333−3000000000000
χ382222-2-2-1-22-2-22-222-1-1-11111-2211-2-2-2-22222-1-111-1-111-1-11111-1-1-1-11111-1-1-1-10000−333−33−3−33000000000000
χ3922-2-22-2222000-2-202-2-222-2-2002-222−2−222−2−22-20000000022−2−222−2−222−2−222−2−20000000000002-2002−22−20000
χ4022-2-22-2222000-2-202-2-222-2-2002-222−2−222−2−22-20000000022−2−222−2−222−2−222−2−2000000000000-2200−22−220000
χ4122-2-22-2222000-2-202-2-222-2-2002-2−2−222−2−2222-200000000−2−222−2−222−2−222−2−2220000000000002-200−22−220000
χ4222-2-22-2222000-2-202-2-222-2-2002-2−2−222−2−2222-200000000−2−222−2−222−2−222−2−222000000000000-22002−22−20000
χ4322-2-2-222-220002-202-2-2-2-22200-2222−2−2−2−2222-20000000022−2−2−2−22222−2−2−2−222000000000000002i−2i−i2i2i2−i20000
χ4422-2-2-222-220002-202-2-2-2-22200-2222−2−2−2−2222-20000000022−2−2−2−22222−2−2−2−22200000000000000−2i2ii2−i2−i2i20000
χ4522-2-2-222-220002-202-2-2-2-22200-22−2−22222−2−22-200000000−2−22222−2−2−2−22222−2−2000000000000002i−2ii2−i2−i2i20000
χ4622-2-2-222-220002-202-2-2-2-22200-22−2−22222−2−22-200000000−2−22222−2−2−2−22222−2−200000000000000−2i2i−i2i2i2−i20000
χ47444444-244-4-4-444-4-2-2-2-2-2-2-2-4-4-2-200000000-2-2222222220000000000000000000000000000000000000000
χ48444444-2-4-4444-4-44-2-2-22222-4-4-2-20000000022-2-2-2-222220000000000000000000000000000000000000000
χ494444-4-4-24-4-4-444-44-2-2-2-2-2-2-24-422000000002222-2-2-2-2220000000000000000000000000000000000000000
χ504444-4-4-2-4444-4-44-4-2-2-222224-42200000000-2-2-2-222-2-2220000000000000000000000000000000000000000
χ5144-4-44-44-4-40004404-4-4-4-444004-400000000-44000000000000000000000000000000000000000000000000
χ5244-4-44-4-244000-4-40-222-2-22200-222222−22−222222−22−22-2200000000−2−222−2−222−2−222−2−222000000000000000000000000
χ5344-4-44-4-244000-4-40-222-2-22200-22−22−222222−22−222222-220000000022−2−222−2−222−2−222−2−2000000000000000000000000
χ5444-4-44-4-2-4-4000440-22222-2-200-22000000002-200000000i6i6−i6−i6i6i6−i6−i6−i6−i6i6i6−i6−i6i6i6000000000000000000000000
χ5544-4-44-4-2-4-4000440-22222-2-200-22000000002-200000000−i6−i6i6i6−i6−i6i6i6i6i6−i6−i6i6i6−i6−i6000000000000000000000000
χ5644-4-4-4444-4000-4404-4-444-4-400-4400000000-44000000000000000000000000000000000000000000000000
χ5744-4-4-44-24-4000-440-222-2-222002-2000000002-200000000i6i6−i6−i6−i6−i6i6i6−i6−i6i6i6i6i6−i6−i6000000000000000000000000
χ5844-4-4-44-24-4000-440-222-2-222002-2000000002-200000000−i6−i6i6i6i6i6−i6−i6i6i6−i6−i6−i6−i6i6i6000000000000000000000000
χ5944-4-4-44-2-440004-40-22222-2-2002-22222−22−22−22−222222-2200000000−2−22222−2−2−2−22222−2−2000000000000000000000000
χ6044-4-4-44-2-440004-40-22222-2-2002-2−22−2222222222−22−22-220000000022−2−2−2−22222−2−2−2−222000000000000000000000000
χ614-44-4004004i−4i0000-44-4000000002-22-22i−2i2i−2i004i−4i0000002-22-22i−2i2i−2i2-22-22i−2i2i−2i000000000000000000000000
χ624-44-4004004i−4i0000-44-400000000-22-22−2i2i−2i2i004i−4i000000-22-22−2i2i−2i2i-22-22−2i2i−2i2i000000000000000000000000
χ634-44-400400−4i4i0000-44-4000000002-22-2−2i2i−2i2i00−4i4i0000002-22-2−2i2i−2i2i2-22-2−2i2i−2i2i000000000000000000000000
χ644-44-400400−4i4i0000-44-400000000-22-222i−2i2i−2i00−4i4i000000-22-222i−2i2i−2i-22-222i−2i2i−2i000000000000000000000000
χ654-44-400-2004i−4i00002-2223−2323−2300002-22-22i−2i2i−2i00−2i2i0000−2i32i3−1−i31+i3−1−i31+i32ζ14−2ζ142ζ14−2ζ14−1+i31−i3−1+i31−i32ζ22−2ζ222ζ22−2ζ22000000000000000000000000
χ664-44-400-2004i−4i00002-2223−2323−230000-22-22−2i2i−2i2i00−2i2i0000−2i32i31+i3−1−i31+i3−1−i3−2ζ142ζ14−2ζ142ζ141−i3−1+i31−i3−1+i3−2ζ222ζ22−2ζ222ζ22000000000000000000000000
χ674-44-400-2004i−4i00002-22−2323−232300002-22-22i−2i2i−2i00−2i2i00002i3−2i3−1+i31−i3−1+i31−i32ζ22−2ζ222ζ22−2ζ22−1−i31+i3−1−i31+i32ζ14−2ζ142ζ14−2ζ14000000000000000000000000
χ684-44-400-2004i−4i00002-22−2323−23230000-22-22−2i2i−2i2i00−2i2i00002i3−2i31−i3−1+i31−i3−1+i3−2ζ222ζ22−2ζ222ζ221+i3−1−i31+i3−1−i3−2ζ142ζ14−2ζ142ζ14000000000000000000000000
χ694-44-400-200−4i4i00002-2223−2323−2300002-22-2−2i2i−2i2i002i−2i00002i3−2i3−1+i31−i3−1+i31−i3−2ζ222ζ22−2ζ222ζ22−1−i31+i3−1−i31+i3−2ζ142ζ14−2ζ142ζ14000000000000000000000000
χ704-44-400-200−4i4i00002-2223−2323−230000-22-222i−2i2i−2i002i−2i00002i3−2i31−i3−1+i31−i3−1+i32ζ22−2ζ222ζ22−2ζ221+i3−1−i31+i3−1−i32ζ14−2ζ142ζ14−2ζ14000000000000000000000000
χ714-44-400-200−4i4i00002-22−2323−232300002-22-2−2i2i−2i2i002i−2i0000−2i32i3−1−i31+i3−1−i31+i3−2ζ142ζ14−2ζ142ζ14−1+i31−i3−1+i31−i3−2ζ222ζ22−2ζ222ζ22000000000000000000000000
χ724-44-400-200−4i4i00002-22−2323−23230000-22-222i−2i2i−2i002i−2i0000−2i32i31+i3−1−i31+i3−1−i32ζ14−2ζ142ζ14−2ζ141−i3−1+i31−i3−1+i32ζ22−2ζ222ζ22−2ζ22000000000000000000000000
χ734-4-440040000400-4-4-44000000000000−2i22i22i2−2i200004-400000000−2i22i22i2−2i20000−2i22i22i2−2i2000000000000000000000000
χ744-4-440040000400-4-4-440000000000002i2−2i2−2i22i200004-4000000002i2−2i2−2i22i200002i2−2i2−2i22i2000000000000000000000000
χ754-4-440040000-4004-4-440000000022−22−222200000000-44000022−22−2222000022−22−22220000000000000000000000000000
χ764-4-440040000-4004-4-4400000000−222222−2200000000-440000−222222−220000−222222−220000000000000000000000000000
χ774-4-4400-20000400-422-223−23−232300000000−2i22i22i2−2i20000-2223−2300i6−i6−i6i6i2−i2−i2i2−i6i6i6−i6i2−i2−i2i2000000000000000000000000
χ784-4-4400-20000400-422-223−23−2323000000002i2−2i2−2i22i20000-2223−2300−i6i6i6−i6−i2i2i2−i2i6−i6−i6i6−i2i2i2−i2000000000000000000000000
χ794-4-4400-20000400-422-2−232323−2300000000−2i22i22i2−2i20000-22−232300−i6i6i6−i6i2−i2−i2i2i6−i6−i6i6i2−i2−i2i2000000000000000000000000
χ804-4-4400-20000400-422-2−232323−23000000002i2−2i2−2i22i20000-22−232300i6−i6−i6i6−i2i2i2−i2−i6i6i6−i6−i2i2i2−i2000000000000000000000000
χ814-4-4400-20000-400422-223−23−2323000022−22−2222000000002-2−232300−222−2−666−6−222−26−6−66000000000000000000000000
χ824-4-4400-20000-400422-223−23−23230000−222222−22000000002-2−2323002−2−226−6−662−2−22−666−6000000000000000000000000
χ834-4-4400-20000-400422-2−232323−23000022−22−2222000000002-223−2300−222−26−6−66−222−2−666−6000000000000000000000000
χ844-4-4400-20000-400422-2−232323−230000−222222−22000000002-223−23002−2−22−666−62−2−226−6−66000000000000000000000000

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