Finite Group Databasebeta

← Group #10692237

Character table — Group #10692237

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size11112222222222222244444444444444448888888888888888888888881212121216161616161624242424242448484848
order12222234444666121212122244666688881212121268888881224242424242424242424242424242424224488242424242488884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-111111-1-111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-111
χ611111111111111111111111111-1-1-1-111111-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ711111111111111111111111111-1-1-1-111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1
χ811111111111111111111111111-1-1-1-111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-111
χ91111-1-1111-1-111111111-11-1-1-1-1-1ii−i−i-1-1-1-11i−iii−i−i1iiii−i−i−i−iiiii−i−i−i−i11-1-11-111-1-1-11ii−i−i1-1i−i
χ101111-1-1111-1-111111111-11-1-1-1-1-1ii−i−i-1-1-1-11i−iii−i−i1iiii−i−i−i−iiiii−i−i−i−i-1-1111-111-1-11-1−i−iii-11−ii
χ111111-1-1111-1-111111111-11-1-1-1-1-1ii−i−i-1-1-1-11i−i−i−iii1iiii−i−i−i−i−i−i−i−iiiii11-1-1-11-1-111-11ii−i−i-11−ii
χ121111-1-1111-1-111111111-11-1-1-1-1-1ii−i−i-1-1-1-11i−i−i−iii1iiii−i−i−i−i−i−i−i−iiiii-1-111-11-1-1111-1−i−iii1-1i−i
χ131111-1-1111-1-111111111-11-1-1-1-1-1−i−iii-1-1-1-11−iiii−i−i1−i−i−i−iiiiiiiii−i−i−i−i11-1-1-11-1-111-11−i−iii-11i−i
χ141111-1-1111-1-111111111-11-1-1-1-1-1−i−iii-1-1-1-11−iiii−i−i1−i−i−i−iiiiiiiii−i−i−i−i-1-111-11-1-1111-1ii−i−i1-1−ii
χ151111-1-1111-1-111111111-11-1-1-1-1-1−i−iii-1-1-1-11−ii−i−iii1−i−i−i−iiiii−i−i−i−iiiii11-1-11-111-1-1-11−i−iii1-1−ii
χ161111-1-1111-1-111111111-11-1-1-1-1-1−i−iii-1-1-1-11−ii−i−iii1−i−i−i−iiiii−i−i−i−iiiii-1-1111-111-1-11-1ii−i−i-11i−i
χ17222222222-2-22222222-2-2-2222-2-2000022-2-2-2000000-2000000000000000022-2-20000002-200000000
χ18222222222-2-22222222-2-2-2222-2-2000022-2-2-2000000-20000000000000000-2-222000000-2200000000
χ192222222-2-222222-2-2-2-2-2-22-222-2-22222-2-222-2-2-20000222-2-222-2-20000000000000000000000000000
χ202222222-2-222222-2-2-2-2-2-22-222-2-2-2-2-2-2-2-222-22200002-2-222-2-2220000000000000000000000000000
χ212222222-2-2-2-2222-2-2-2-222-2-222220000-2-2-2-22000000-200000000000000000000000000002i−2i2i−2i0000
χ222222222-2-2-2-2222-2-2-2-222-2-222220000-2-2-2-22000000-20000000000000000000000000000−2i2i−2i2i0000
χ23222222-12222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-10000000000
χ24222222-12222-1-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1111111110000-2-211110000000000
χ25222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-1-1-2-22222-111111111-1-1-1-1-1-1-1-10000-2-211110000000000
χ26222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-1-1-2-2-2-2-2-2-11111111111111111000022-1-1-1-10000000000
χ27222222-1-2-222-1-1-11111-2-22-2-1-111222211-1-11-2-20000-1-1-111-1-11133−3−333−3−30000003−33−30000000000
χ28222222-1-2-222-1-1-11111-2-22-2-1-111222211-1-11-2-20000-1-1-111-1-111−3−333−3−333000000−33−330000000000
χ29222222-1-2-222-1-1-11111-2-22-2-1-111-2-2-2-211-1-11220000-111-1-111-1-133−3−333−3−3000000−33−330000000000
χ30222222-1-2-222-1-1-11111-2-22-2-1-111-2-2-2-211-1-11220000-111-1-111-1-1−3−333−3−3330000003−33−30000000000
χ312222-2-2222222222222-22-2-2-2-2220000-2-222-2000000-200000000000000002222000000-2-200000000
χ322222-2-2222222222222-22-2-2-2-2220000-2-222-2000000-20000000000000000-2-2-2-20000002200000000
χ332222-2-22-2-222222-2-2-2-22-2-22-2-2-2-2000022222000000-200000000000000000000000000002-2-220000
χ342222-2-22-2-222222-2-2-2-22-2-22-2-2-2-2000022222000000-20000000000000000000000000000-222-20000
χ352222-2-22-2-2-2-2222-2-2-2-2-2222-2-2222i2i−2i−2i22-2-2-2−2i2i000022i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ362222-2-22-2-2-2-2222-2-2-2-2-2222-2-222−2i−2i2i2i22-2-2-22i−2i00002−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ372222-2-2-122-2-2-1-1-1-1-1-1-12-22-211112i2i−2i−2i1111-12i−2i2i2i−2i−2i-1−i−i−i−iiiii−i−i−i−iiiii00002-2-1-1110000000000
χ382222-2-2-122-2-2-1-1-1-1-1-1-12-22-211112i2i−2i−2i1111-12i−2i−2i−2i2i2i-1−i−i−i−iiiiiiiii−i−i−i−i0000-2211-1-10000000000
χ392222-2-2-122-2-2-1-1-1-1-1-1-12-22-21111−2i−2i2i2i1111-1−2i2i2i2i−2i−2i-1iiii−i−i−i−i−i−i−i−iiiii0000-2211-1-10000000000
χ402222-2-2-122-2-2-1-1-1-1-1-1-12-22-21111−2i−2i2i2i1111-1−2i2i−2i−2i2i2i-1iiii−i−i−i−iiiii−i−i−i−i00002-2-1-1110000000000
χ412222-2-2-1-2-2-2-2-1-1-11111-222211-1-12i2i−2i−2i-1-1111−2i2i0000-1−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i3000000−333−30000000000
χ422222-2-2-1-2-2-2-2-1-1-11111-222211-1-12i2i−2i−2i-1-1111−2i2i0000-1−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i30000003−3−330000000000
χ432222-2-2-1-2-2-2-2-1-1-11111-222211-1-1−2i−2i2i2i-1-11112i−2i0000-1ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i30000003−3−330000000000
χ442222-2-2-1-2-2-2-2-1-1-11111-222211-1-1−2i−2i2i2i-1-11112i−2i0000-1ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i3000000−333−30000000000
χ45444444-244-4-4-2-2-2-2-2-2-2-4-4-44-2-2220000-2-22220000002000000000000000000000000000000000000
χ46444444-2-4-4-4-4-2-2-2222244-4-4-2-2-2-200002222-20000002000000000000000000000000000000000000
χ474444-4-4-24444-2-2-2-2-2-2-2-44-4-422-2-2000022-2-220000002000000000000000000000000000000000000
χ484444-4-4-2-4-444-2-2-222224-4-4422220000-2-2-2-2-20000002000000000000000000000000000000000000
χ4944-4-44-4400004-4-4000000004-40022−2222−2200000000000022−220022−22000000000000000000000000000000
χ5044-4-44-4400004-4-4000000004-400−2222−2222000000000000−222200−2222000000000000000000000000000000
χ5144-4-44-4-20000-2222323−23−230000-220022−2222−2223−230000000000−226−6−226−60000000000000000000000000000
χ5244-4-44-4-20000-2222323−23−230000-2200−2222−222223−2300000000002−2−662−2−660000000000000000000000000000
χ5344-4-44-4-20000-222−23−2323230000-220022−2222−22−23230000000000−22−66−22−660000000000000000000000000000
χ5444-4-44-4-20000-222−23−2323230000-2200−2222−2222−232300000000002−26−62−26−60000000000000000000000000000
χ5544-4-4-44400004-4-400000000-4400−2i22i22i2−2i2000000000000−2i22i2002i2−2i2000000000000000000000000000000
χ5644-4-4-44400004-4-400000000-44002i2−2i2−2i22i20000000000002i2−2i200−2i22i2000000000000000000000000000000
χ5744-4-4-44-20000-2222323−23−2300002-200−2i22i22i2−2i2−23230000000000i2−i2−i6i6−i2i2i6−i60000000000000000000000000000
χ5844-4-4-44-20000-2222323−23−2300002-2002i2−2i2−2i22i2−23230000000000−i2i2i6−i6i2−i2−i6i60000000000000000000000000000
χ5944-4-4-44-20000-222−23−23232300002-200−2i22i22i2−2i223−230000000000i2−i2i6−i6−i2i2−i6i60000000000000000000000000000
χ6044-4-4-44-20000-222−23−23232300002-2002i2−2i2−2i22i223−230000000000−i2i2−i6i6i2−i2i6−i60000000000000000000000000000
χ614-44-4004004i−4i-44-40000000000000000004i−4i0002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ624-44-4004004i−4i-44-40000000000000000004i−4i000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ634-44-400400−4i4i-44-4000000000000000000−4i4i000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ644-44-400400−4i4i-44-4000000000000000000−4i4i0002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ654-44-400-2004i−4i2-2223−2323−23000000−2i32i3000000−2i2i0002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ2300000000000000000000
χ664-44-400-2004i−4i2-2223−2323−23000000−2i32i3000000−2i2i000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ2300000000000000000000
χ674-44-400-2004i−4i2-22−2323−23230000002i3−2i3000000−2i2i0002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000000−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ2300000000000000000000
χ684-44-400-2004i−4i2-22−2323−23230000002i3−2i3000000−2i2i000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000000ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ2300000000000000000000
χ694-44-400-200−4i4i2-2223−2323−230000002i3−2i30000002i−2i000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ2300000000000000000000
χ704-44-400-200−4i4i2-2223−2323−230000002i3−2i30000002i−2i0002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ2300000000000000000000
χ714-44-400-200−4i4i2-22−2323−2323000000−2i32i30000002i−2i000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000000ζ5+ζ7+ζ13−ζ23−ζ5−ζ7−ζ13+ζ23ζ5−ζ7+ζ13+ζ23−ζ5+ζ7−ζ13−ζ23−ζ5−ζ7+ζ13−ζ23ζ5+ζ7−ζ13+ζ23ζ5−ζ7−ζ13−ζ23−ζ5+ζ7+ζ13+ζ2300000000000000000000
χ724-44-400-200−4i4i2-22−2323−2323000000−2i32i30000002i−2i0002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000000−ζ5−ζ7−ζ13+ζ23ζ5+ζ7+ζ13−ζ23−ζ5+ζ7−ζ13−ζ23ζ5−ζ7+ζ13+ζ23ζ5+ζ7−ζ13+ζ23−ζ5−ζ7+ζ13−ζ23−ζ5+ζ7+ζ13+ζ23ζ5−ζ7−ζ13−ζ2300000000000000000000
χ734-4-440044-400-4-444-4-4400000000000000000000000000000000000000004-4000000000000000000
χ744-4-440044-400-4-444-4-440000000000000000000000000000000000000000-44000000000000000000
χ754-4-44004-4400-4-44-444-40000000000000000000000000000000000000000004-40000000000000000
χ764-4-44004-4400-4-44-444-4000000000000000000000000000000000000000000-440000000000000000
χ778-8-8800-48-80044-4-444-4000000000000000000000000000000000000000000000000000000000000
χ788-8-8800-4-880044-44-4-44000000000000000000000000000000000000000000000000000000000000

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