Finite Group Databasebeta

← Group #68675

Character table — Group #68675

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11111111222222222222222222224444444444444444444444444444444444442424242424242424
order12222222344446666666121212121212121244448888888812121212121212122424242424242424242424242424242422224444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ51111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ9222222222-2-2-2-22222222-2-2-2-2-2-2-2-222-2-2000000002222-2-2-2-2000000000000000000000000
χ10222222222-2-2-2-22222222-2-2-2-2-2-2-2-2-2-22200000000-2-2-2-22222000000000000000000000000
χ1122222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000
χ1222222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1111111111111111100000000
χ1322222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-2-2-2-211111111-1-1-1-1-1-1-1-11111111100000000
χ1422222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222221111111111111111-1-1-1-1-1-1-1-100000000
χ1522222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-200000000-1-1-1-111113333−3−3−3−33333−3−3−3−300000000
χ1622222222-1-2-2-2-2-1-1-1-1-1-1-11111111122-2-200000000-1-1-1-11111−3−3−3−33333−3−3−3−3333300000000
χ1722222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-222000000001111-1-1-1-13333−3−3−3−3−3−3−3−3333300000000
χ1822222222-1-2-2-2-2-1-1-1-1-1-1-111111111-2-222000000001111-1-1-1-1−3−3−3−333333333−3−3−3−300000000
χ19222-22-2-2-22000022-2-22-2-200000000002i−2i22−2−2−i2−i2i2i200002i2i−2i−2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i200000000
χ20222-22-2-2-22000022-2-22-2-200000000002i−2i−2−222i2i2−i2−i200002i2i−2i−2i−2−222−2−222i2i2−i2−i2i2i2−i2−i200000000
χ21222-22-2-2-22000022-2-22-2-20000000000−2i2i22−2−2i2i2−i2−i20000−2i−2i2i2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i200000000
χ22222-22-2-2-22000022-2-22-2-20000000000−2i2i−2−222−i2−i2i2i20000−2i−2i2i2i−2−222−2−222−i2−i2i2i2−i2−i2i2i200000000
χ23222-22-2-2-2-10000-1-111-11133−3−333−3−3002i−2i22−2−2−i2−i2i2i2−i3−i3i3i3−i−iiiζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300000000
χ24222-22-2-2-2-10000-1-111-11133−3−333−3−3002i−2i−2−222i2i2−i2−i2−i3−i3i3i3−i−iii−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300000000
χ25222-22-2-2-2-10000-1-111-11133−3−333−3−300−2i2i22−2−2i2i2−i2−i2i3i3−i3−i3ii−i−iζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ2300000000
χ26222-22-2-2-2-10000-1-111-11133−3−333−3−300−2i2i−2−222−i2−i2i2i2i3i3−i3−i3ii−i−i−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ2300000000
χ27222-22-2-2-2-10000-1-111-111−3−333−3−333002i−2i22−2−2−i2−i2i2i2i3i3−i3−i3−i−iiiζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700000000
χ28222-22-2-2-2-10000-1-111-111−3−333−3−333002i−2i−2−222i2i2−i2−i2i3i3−i3−i3−i−iii−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700000000
χ29222-22-2-2-2-10000-1-111-111−3−333−3−33300−2i2i22−2−2i2i2−i2−i2−i3−i3i3i3ii−i−iζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7−ζ13−ζ23−ζ13−ζ23ζ13+ζ23ζ13+ζ23−ζ5−ζ7−ζ5−ζ7ζ5+ζ7ζ5+ζ700000000
χ30222-22-2-2-2-10000-1-111-111−3−333−3−33300−2i2i−2−222−i2−i2i2i2−i3−i3i3i3ii−i−i−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7ζ13+ζ23ζ13+ζ23−ζ13−ζ23−ζ13−ζ23ζ5+ζ7ζ5+ζ7−ζ5−ζ7−ζ5−ζ700000000
χ3122-22-22-2-2200002-22-2-22-2000000002i−2i002−22−2−i2i2−i2i22i−2i2i−2i00002−22−22−22−2−i2i2−i2i2−i2i2−i2i200000000
χ3222-22-22-2-2200002-22-2-22-2000000002i−2i00−22−22i2−i2i2−i22i−2i2i−2i0000−22−22−22−22i2−i2i2−i2i2−i2i2−i200000000
χ3322-22-22-2-2200002-22-2-22-200000000−2i2i002−22−2i2−i2i2−i2−2i2i−2i2i00002−22−22−22−2i2−i2i2−i2i2−i2i2−i200000000
χ3422-22-22-2-2200002-22-2-22-200000000−2i2i00−22−22−i2i2−i2i2−2i2i−2i2i0000−22−22−22−22−i2i2−i2i2−i2i2−i2i200000000
χ3522-22-22-2-2-10000-11-111-113−33−33−33−32i−2i002−22−2−i2i2−i2i2−ii−ii−i3i3−i3i3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ700000000
χ3622-22-22-2-2-10000-11-111-113−33−33−33−32i−2i00−22−22i2−i2i2−i2−ii−ii−i3i3−i3i3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ700000000
χ3722-22-22-2-2-10000-11-111-113−33−33−33−3−2i2i002−22−2i2−i2i2−i2i−ii−ii3−i3i3−i3ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ700000000
χ3822-22-22-2-2-10000-11-111-113−33−33−33−3−2i2i00−22−22−i2i2−i2i2i−ii−ii3−i3i3−i3−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ700000000
χ3922-22-22-2-2-10000-11-111-11−33−33−33−332i−2i002−22−2−i2i2−i2i2−ii−iii3−i3i3−i3ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ2300000000
χ4022-22-22-2-2-10000-11-111-11−33−33−33−332i−2i00−22−22i2−i2i2−i2−ii−iii3−i3i3−i3−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ2300000000
χ4122-22-22-2-2-10000-11-111-11−33−33−33−33−2i2i002−22−2i2−i2i2−i2i−ii−i−i3i3−i3i3ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ2300000000
χ4222-22-22-2-2-10000-11-111-11−33−33−33−33−2i2i00−22−22−i2i2−i2i2i−ii−i−i3i3−i3i3−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ2300000000
χ4322-2-2-2-22222-22-22-2-22-2-222-2-222-2-2200002-2-220000000000002-2-222-2-220000000000000000
χ4422-2-2-2-22222-22-22-2-22-2-222-2-222-2-220000-222-2000000000000-222-2-222-20000000000000000
χ4522-2-2-2-2222-22-222-2-22-2-22-222-2-222-2000000002-2-2200000000000000002-2-222-2-2200000000
χ4622-2-2-2-2222-22-222-2-22-2-22-222-2-222-200000000-222-20000000000000000-222-2-222-200000000
χ4722-2-2-2-222-12-22-2-111-111-1-111-1-111-100002-2-2200003−3−33−333−3-111-1-111-13−3−33−333−300000000
χ4822-2-2-2-222-12-22-2-111-111-1-111-1-111-100002-2-220000−333−33−3−33-111-1-111-1−333−33−3−3300000000
χ4922-2-2-2-222-12-22-2-111-111-1-111-1-111-10000-222-200003−3−33−333−31-1-111-1-11−333−33−3−3300000000
χ5022-2-2-2-222-12-22-2-111-111-1-111-1-111-10000-222-20000−333−33−3−331-1-111-1-113−3−33−333−300000000
χ5122-2-2-2-222-1-22-22-111-111-11-1-111-1-11000000002-2-223−3−333−3−33−333−33−3−33-111-1-111-100000000
χ5222-2-2-2-222-1-22-22-111-111-11-1-111-1-11000000002-2-22−333−3−333−33−3−33−333−3-111-1-111-100000000
χ5322-2-2-2-222-1-22-22-111-111-11-1-111-1-1100000000-222-23−3−333−3−333−3−33−333−31-1-111-1-1100000000
χ5422-2-2-2-222-1-22-22-111-111-11-1-111-1-1100000000-222-2−333−3−333−3−333−33−3−331-1-111-1-1100000000
χ552-222-2-2-22222-2-2-222-2-2-222222-2-2-2-200000000000000000000000000000000000000002i−2i00
χ562-222-2-2-22222-2-2-222-2-2-222222-2-2-2-20000000000000000000000000000000000000000−2i2i00
χ572-222-2-2-222-2-222-222-2-2-22-2-2-2-222220000000000000000000000000000000000002-2000000
χ582-222-2-2-222-2-222-222-2-2-22-2-2-2-22222000000000000000000000000000000000000-22000000
χ592-2-2-222-2222-2-22-2-2-2-22222-2-22-222-20000000000000000000000000000000000000000002-2
χ602-2-2-222-2222-2-22-2-2-2-22222-2-22-222-2000000000000000000000000000000000000000000-22
χ612-2-2-222-222-222-2-2-2-2-2222-222-22-2-22000000000000000000000000000000000000002-20000
χ622-2-2-222-222-222-2-2-2-2-2222-222-22-2-2200000000000000000000000000000000000000-220000
χ634-444-4-4-44-244-4-42-2-2222-2-2-2-2-2222200000000000000000000000000000000000000000000
χ644-444-4-4-44-2-4-4442-2-2222-22222-2-2-2-200000000000000000000000000000000000000000000
χ654-44-4-444-440000-44-44-44-40000000000000000000000000000000000000000000000000000
χ664-44-4-444-4-200002-22-22-222323−23−23−23−23232300000000000000000000000000000000000000000000
χ674-44-4-444-4-200002-22-22-22−23−2323232323−23−2300000000000000000000000000000000000000000000
χ684-4-444-44-440000-4-4444-4-40000000000000000000000000000000000000000000000000000
χ694-4-444-44-4-2000022-2-2-22223−2323−23−2323−232300000000000000000000000000000000000000000000
χ704-4-444-44-4-2000022-2-2-222−2323−232323−2323−2300000000000000000000000000000000000000000000
χ714-4-4-444-44-24-4-442222-2-2-2-222-22-2-2200000000000000000000000000000000000000000000
χ724-4-4-444-44-2-444-42222-2-2-22-2-22-222-200000000000000000000000000000000000000000000

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