Finite Group Databasebeta

← Group #10698971

Character table — Group #10698971

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size1111222222222222222244444444444444488888888888888888888888888888888888824242424484848484848
order12222234444446661212121244466121212121212121212124444888888881212121212121212242424242424242424242424242424248888444488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ511111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ611111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111
χ811111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ92222222222-2-22222-2-2-2-2-2-2-222-2-22222-2-2-2-222-2-2000000002222-2-2-2-200000000000000000000000000
χ102222222222-2-22222-2-2-2-2-2-2-222-2-22222-2-2-2-2-2-22200000000-2-2-2-2222200000000000000000000000000
χ112222222-2-2-222-222222222-2-22222-2-2-2-2-2-2-2-200002i2i−2i−2i0000000000002i2i2i2i−2i−2i−2i−2i000000000000000000
χ122222222-2-2-222-222222222-2-22222-2-2-2-2-2-2-2-20000−2i−2i2i2i000000000000−2i−2i−2i−2i2i2i2i2i000000000000000000
χ132222222-2-2-2-2-2-2222-2-2-2-2-22222-2-2-2-2-2-222220000000022-2-200000000000000002222-2-2-2-20000000000
χ142222222-2-2-2-2-2-2222-2-2-2-2-22222-2-2-2-2-2-2222200000000-2-2220000000000000000-2-2-2-222220000000000
χ15222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000
χ16222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111110000000000
χ17222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-1111111110000000000
χ18222222-1222222-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-10000000000
χ19222222-1222-2-22-1-1-11111-2-2-2-1-111-1-1-1-1111122-2-200000000-1-1-1-1111133−3−333−3−333−3−333−3−30000000000
χ20222222-1222-2-22-1-1-11111-2-2-2-1-111-1-1-1-1111122-2-200000000-1-1-1-11111−3−333−3−333−3−333−3−3330000000000
χ21222222-1222-2-22-1-1-11111-2-2-2-1-111-1-1-1-11111-2-222000000001111-1-1-1-133−3−333−3−3−3−333−3−3330000000000
χ22222222-1222-2-22-1-1-11111-2-2-2-1-111-1-1-1-11111-2-222000000001111-1-1-1-1−3−333−3−33333−3−333−3−30000000000
χ23222222-1-2-2-222-2-1-1-1-1-1-1-12-2-2-1-1-1-11111111100002i2i−2i−2i0000−i3−i3i3i3−i3−i3i3i3−i−i−i−iiiii33−3−3−3−3330000000000
χ24222222-1-2-2-222-2-1-1-1-1-1-1-12-2-2-1-1-1-11111111100002i2i−2i−2i0000i3i3−i3−i3i3i3−i3−i3−i−i−i−iiiii−3−33333−3−30000000000
χ25222222-1-2-2-222-2-1-1-1-1-1-1-12-2-2-1-1-1-1111111110000−2i−2i2i2i0000−i3−i3i3i3−i3−i3i3i3iiii−i−i−i−i−3−33333−3−30000000000
χ26222222-1-2-2-222-2-1-1-1-1-1-1-12-2-2-1-1-1-1111111110000−2i−2i2i2i0000i3i3−i3−i3i3i3−i3−i3iiii−i−i−i−i33−3−3−3−3330000000000
χ27222222-1-2-2-2-2-2-2-1-1-11111-222-1-1111111-1-1-1-10000000022-2-2−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-1-1-1-111110000000000
χ28222222-1-2-2-2-2-2-2-1-1-11111-222-1-1111111-1-1-1-10000000022-2-2i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3-1-1-1-111110000000000
χ29222222-1-2-2-2-2-2-2-1-1-11111-222-1-1111111-1-1-1-100000000-2-222−i3−i3i3i3i3i3−i3−i3i3i3−i3−i3−i3−i3i3i31111-1-1-1-10000000000
χ30222222-1-2-2-2-2-2-2-1-1-11111-222-1-1111111-1-1-1-100000000-2-222i3i3−i3−i3−i3−i3i3i3−i3−i3i3i3i3i3−i3−i31111-1-1-1-10000000000
χ312222-2-2222-222-22222222-22-2-2-2-2-222-2-222-2-20000000000000000000000000000000000000000002i−2i00
χ322222-2-2222-222-22222222-22-2-2-2-2-222-2-222-2-2000000000000000000000000000000000000000000−2i2i00
χ332222-2-2222-2-2-2-2222-2-2-2-22-22-2-22222-2-2-2-2220000000000000000000000000000000000002i2i−2i−2i000000
χ342222-2-2222-2-2-2-2222-2-2-2-22-22-2-22222-2-2-2-222000000000000000000000000000000000000−2i−2i2i2i000000
χ352222-2-22-2-222222222222-2-22-2-2-2-2-2-222-2-222000000000000000000000000000000000000000000002-2
χ362222-2-22-2-222222222222-2-22-2-2-2-2-2-222-2-22200000000000000000000000000000000000000000000-22
χ372222-2-22-2-22-2-22222-2-2-2-222-2-2-222-2-22222-2-200000000000000000000000000000000000000002-20000
χ382222-2-22-2-22-2-22222-2-2-2-222-2-2-222-2-22222-2-20000000000000000000000000000000000000000-220000
χ3922-2-22-222-2200-2-22-200000002-2002-22-200002-2002−22−22−22−22-22-200002−22−22−22−22−22−22−22−20000000000
χ4022-2-22-222-2200-2-22-200000002-2002-22-200002-200−22−22−22−222-22-20000−22−22−22−22−22−22−22−220000000000
χ4122-2-22-222-2200-2-22-200000002-2002-22-20000-22002−22−2−22−22-22-2200002−22−22−22−2−22−22−22−220000000000
χ4222-2-22-222-2200-2-22-200000002-2002-22-20000-2200−22−222−22−2-22-220000−22−22−22−222−22−22−22−20000000000
χ4322-2-22-22-22-2002-22-200000002-200-22-220000002i−2i−i2i2i2−i22−2−2200002i−2i2i−2i−i2i2−i2i2i2−i2i2−i22−22−2−22−220000000000
χ4422-2-22-22-22-2002-22-200000002-200-22-220000002i−2ii2−i2−i2i2−222−200002i−2i2i−2ii2−i2i2−i2−i2i2−i2i2−22−222−22−20000000000
χ4522-2-22-22-22-2002-22-200000002-200-22-22000000−2i2i−i2i2i2−i2−222−20000−2i2i−2i2i−i2i2−i2i2i2−i2i2−i2−22−222−22−20000000000
χ4622-2-22-22-22-2002-22-200000002-200-22-22000000−2i2ii2−i2−i2i22−2−220000−2i2i−2i2ii2−i2i2−i2−i2i2−i2i22−22−2−22−220000000000
χ4722-2-22-2-12-2200-21-1133−3−3000-113−3-11-113−33−32-2002−22−22−22−2-11-113−3−33ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000
χ4822-2-22-2-12-2200-21-1133−3−3000-113−3-11-113−33−32-200−22−22−22−22-11-113−3−33−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000
χ4922-2-22-2-12-2200-21-1133−3−3000-113−3-11-113−33−3-22002−22−2−22−221-11-1−333−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000
χ5022-2-22-2-12-2200-21-1133−3−3000-113−3-11-113−33−3-2200−22−222−22−21-11-1−333−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000
χ5122-2-22-2-12-2200-21-11−3−333000-11−33-11-11−33−332-2002−22−22−22−2-11-11−333−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000
χ5222-2-22-2-12-2200-21-11−3−333000-11−33-11-11−33−332-200−22−22−22−22-11-11−333−3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000
χ5322-2-22-2-12-2200-21-11−3−333000-11−33-11-11−33−33-22002−22−2−22−221-11-13−3−33ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000
χ5422-2-22-2-12-2200-21-11−3−333000-11−33-11-11−33−33-2200−22−222−22−21-11-13−3−33−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000
χ5522-2-22-2-1-22-20021-1133−3−3000-113−31-11-1−33−33002i−2i−i2i2i2−i22−2−22−i3i3i3−i3−ii−iiζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000
χ5622-2-22-2-1-22-20021-1133−3−3000-113−31-11-1−33−33002i−2ii2−i2−i2i2−222−2−i3i3i3−i3−ii−ii−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000
χ5722-2-22-2-1-22-20021-1133−3−3000-113−31-11-1−33−3300−2i2i−i2i2i2−i2−222−2i3−i3−i3i3i−ii−iζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000000
χ5822-2-22-2-1-22-20021-1133−3−3000-113−31-11-1−33−3300−2i2ii2−i2−i2i22−2−22i3−i3−i3i3i−ii−i−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000000
χ5922-2-22-2-1-22-20021-11−3−333000-11−331-11-13−33−3002i−2i−i2i2i2−i22−2−22i3−i3−i3i3−ii−iiζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000
χ6022-2-22-2-1-22-20021-11−3−333000-11−331-11-13−33−3002i−2ii2−i2−i2i2−222−2i3−i3−i3i3−ii−ii−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000
χ6122-2-22-2-1-22-20021-11−3−333000-11−331-11-13−33−300−2i2i−i2i2i2−i2−222−2−i3i3i3−i3i−ii−iζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000000
χ6222-2-22-2-1-22-20021-11−3−333000-11−331-11-13−33−300−2i2ii2−i2−i2i22−2−22−i3i3i3−i3i−ii−i−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000000
χ634444-4-4-244-444-4-2-2-2-2-2-2-2-44-42222-2-222-2-2220000000000000000000000000000000000000000000000
χ644444-4-4-244-4-4-4-4-2-2-222224-4422-2-2-2-22222-2-20000000000000000000000000000000000000000000000
χ654444-4-4-2-4-44444-2-2-2-2-2-2-2-4-44222222-2-222-2-20000000000000000000000000000000000000000000000
χ664444-4-4-2-4-44-4-44-2-2-2222244-422-2-222-2-2-2-2220000000000000000000000000000000000000000000000
χ6744-4-4-4444-4-4004-44-40000000-44004-4-4400000000000000000000000000000000000000000000000000
χ6844-4-4-444-44400-4-44-40000000-4400-444-400000000000000000000000000000000000000000000000000
χ6944-4-4-44-24-4-40042-222323−23−230002-2−2323-222-223−23−23230000000000000000000000000000000000000000000000
χ7044-4-4-44-24-4-40042-22−23−2323230002-223−23-222-2−232323−230000000000000000000000000000000000000000000000
χ7144-4-4-44-2-44400-42-222323−23−230002-2−23232-2-22−232323−230000000000000000000000000000000000000000000000
χ7244-4-4-44-2-44400-42-22−23−2323230002-223−232-2-2223−23−23230000000000000000000000000000000000000000000000
χ734-4-440040004i−4i0-4-444i−4i4i−4i0000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000
χ744-4-440040004i−4i0-4-444i−4i4i−4i000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000
χ754-4-44004000−4i4i0-4-44−4i4i−4i4i000000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000
χ764-4-44004000−4i4i0-4-44−4i4i−4i4i0000000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000
χ778-88-80080000008-8-800000000000000000000000000000000000000000000000000000000000000000
χ788-88-800-4000000-444−4i34i34i3−4i30000000000000000000000000000000000000000000000000000000000000
χ798-88-800-4000000-4444i3−4i3−4i34i30000000000000000000000000000000000000000000000000000000000000
χ808-8-8800-40008i−8i044-4−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000
χ818-8-8800-4000−8i8i044-44i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000

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