Finite Group Databasebeta

← Group #10714572

Character table — Group #10714572

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order122222344446668888668812121212242424241616161624244848484848484848444488882266668824242424161616164444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-111-1-1
χ7111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1
χ8111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111
χ922222222222222-2-2-2-222-2-22222-2-2-2-20000-2-2000000002222-2-2-2-200000000000000000000
χ1022222222222222-2-2-2-222-2-22222-2-2-2-20000-2-200000000-2-2-2-2222200000000000000000000
χ11222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-122-1-1-1-100000000
χ12222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-21111-2-2111100000000
χ13222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-1-2-2-2-2-1-1111111110000000022-1-1-1-1-2-2111100000000
χ14222222-12222-1-1-12222-1-122-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111100000000-2-2111122-1-1-1-100000000
χ152222-2-222-22-22222222-2-2-2-22-22-222220000-2-2000000000000000000000000000000002-200
χ162222-2-222-22-22222222-2-2-2-22-22-222220000-2-200000000000000000000000000000000-2200
χ172222-2-222-22-2222-2-2-2-2-2-2222-22-2-2-2-2-200002200000000000000000000002i−2i2i2i−2i−2i00000000
χ182222-2-222-22-2222-2-2-2-2-2-2222-22-2-2-2-2-20000220000000000000000000000−2i2i−2i−2i2i2i00000000
χ192222-2-22-22-222220000-2-200-22-22000022−2−2002222−2−2−2−2000022-2-200000000000022−2−20000
χ202222-2-22-22-222220000-2-200-22-22000022−2−2002222−2−2−2−20000-2-222000000000000−2−2220000
χ212222-2-22-22-222220000-2-200-22-220000−2−22200−2−2−2−22222000022-2-2000000000000−2−2220000
χ222222-2-22-22-222220000-2-200-22-220000−2−22200−2−2−2−222220000-2-22200000000000022−2−20000
χ232222-2-2-12-22-2-1-1-1-2-2-2-21122-11-1111110000-1-133−3−333−3−30000000000−i3−i3i3i32i−2i−i−iii00000000
χ242222-2-2-12-22-2-1-1-1-2-2-2-21122-11-1111110000-1-133−3−333−3−30000000000i3i3−i3−i3−2i2iii−i−i00000000
χ252222-2-2-12-22-2-1-1-1-2-2-2-21122-11-1111110000-1-1−3−333−3−3330000000000−i3−i3i3i3−2i2iii−i−i00000000
χ262222-2-2-12-22-2-1-1-1-2-2-2-21122-11-1111110000-1-1−3−333−3−3330000000000i3i3−i3−i32i−2i−i−iii00000000
χ272-2-222-22-222-2-2-2222-2-22-22-2-222-2-2-22200002-200000000000000000000000000002i−2i2i−2i0000
χ282-2-222-22-222-2-2-2222-2-22-22-2-222-2-2-22200002-20000000000000000000000000000−2i2i−2i2i0000
χ292-2-222-22-222-2-2-22-2-2222-2-22-222-222-2-22i−2i2i−2i-222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ302-2-222-22-222-2-2-22-2-2222-2-22-222-222-2-2−2i2i−2i2i-22−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ312-2-222-2-1-222-211-1-2-222-11-221-1-11-1-1112i−2i2i−2i1-1−ii−ii−ii−ii0000000000−i3i3−i3i3003−33−300000000
χ322-2-222-2-1-222-211-1-2-222-11-221-1-11-1-1112i−2i2i−2i1-1−ii−ii−ii−ii0000000000i3−i3i3−i300−33−3300000000
χ332-2-222-2-1-222-211-1-2-222-11-221-1-11-1-111−2i2i−2i2i1-1i−ii−ii−ii−i0000000000−i3i3−i3i300−33−3300000000
χ342-2-222-2-1-222-211-1-2-222-11-221-1-11-1-111−2i2i−2i2i1-1i−ii−ii−ii−i0000000000i3−i3i3−i3003−33−300000000
χ352-2-22-22222-2-2-2-220000-220022-2-20000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i222-2-20000000000000000−i2i2i2−i20000
χ362-2-22-22222-2-2-2-220000-220022-2-20000−i2i2i2−i200−i2i2−i2i2i2−i2i2−i2-2-2220000000000000000i2−i2−i2i20000
χ372-2-22-22222-2-2-2-220000-220022-2-20000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i222-2-20000000000000000i2−i2−i2i20000
χ382-2-22-22222-2-2-2-220000-220022-2-20000i2−i2−i2i200i2−i2i2−i2−i2i2−i2i2-2-2220000000000000000−i2i2i2−i20000
χ392-2-22-222-2-222-2-2222-2-2-22-22-2-222-2-2220000-2200000000000000002-22-2-2200000000000000
χ402-2-22-222-2-222-2-2222-2-2-22-22-2-222-2-2220000-220000000000000000-22-222-200000000000000
χ412-2-22-222-2-222-2-22-2-222-222-2-2-22222-2-200002-200000000000000000000000000000000002-2
χ422-2-22-222-2-222-2-22-2-222-222-2-2-22222-2-200002-20000000000000000000000000000000000-22
χ432-2-22-22-1-2-22211-122-2-21-1-2211-1-111-1-100001-1−i3i3i3−i3−i3i3i3−i3000000002-2-111-100−i3i3i3−i300000000
χ442-2-22-22-1-2-22211-122-2-21-1-2211-1-111-1-100001-1−i3i3i3−i3−i3i3i3−i300000000-221-1-1100i3−i3−i3i300000000
χ452-2-22-22-1-2-22211-122-2-21-1-2211-1-111-1-100001-1i3−i3−i3i3i3−i3−i3i3000000002-2-111-100i3−i3−i3i300000000
χ462-2-22-22-1-2-22211-122-2-21-1-2211-1-111-1-100001-1i3−i3−i3i3i3−i3−i3i300000000-221-1-1100−i3i3i3−i300000000
χ474444444-4-4-4-444400004400-4-4-4-40000000000000000000000000000000000000000000000
χ48444444-24444-2-2-2-4-4-4-4-2-2-4-4-2-2-2-22222000022000000000000000000000000000000000000
χ49444444-2-4-4-4-4-2-2-20000-2-2002222000000000066−6−6−6−6660000000000000000000000000000
χ50444444-2-4-4-4-4-2-2-20000-2-20022220000000000−6−66666−6−60000000000000000000000000000
χ514444-4-4-24-44-4-2-2-2444422-4-4-22-22-2-2-2-2000022000000000000000000000000000000000000
χ524444-4-4-2-44-44-2-2-2000022002-22-200002222−22−2200−2−2−2−222220000000000000000000000000000
χ534444-4-4-2-44-44-2-2-2000022002-22-20000−22−222222002222−2−2−2−20000000000000000000000000000
χ5444-4-400400004-4-422−2222−220000000022−2222−22000000000000002i−2i2i−2i00−2i22i200000000000000000000
χ5544-4-400400004-4-422−2222−220000000022−2222−2200000000000000−2i2i−2i2i002i2−2i200000000000000000000
χ5644-4-400400004-4-4−2222−222200000000−2222−2222000000000000002i−2i2i−2i002i2−2i200000000000000000000
χ5744-4-400400004-4-4−2222−222200000000−2222−222200000000000000−2i2i−2i2i00−2i22i200000000000000000000
χ584-44-40040000-44-422−22−222200000000−222222−22000000000000002i−2i−2i2i−2i22i20000000000000000000000
χ594-44-40040000-44-422−22−222200000000−222222−2200000000000000−2i2i2i−2i2i2−2i20000000000000000000000
χ604-44-40040000-44-4−222222−220000000022−22−2222000000000000002i−2i−2i2i2i2−2i20000000000000000000000
χ614-44-40040000-44-4−222222−220000000022−22−222200000000000000−2i2i2i−2i−2i22i20000000000000000000000
χ624-4-444-444-4-44-4-4400004-4004-4-440000000000000000000000000000000000000000000000
χ634-4-444-4-24-4-4422-20000-2200-222-20000000000i6−i6−i6i6−i6i6i6−i60000000000000000000000000000
χ644-4-444-4-24-4-4422-20000-2200-222-20000000000−i6i6i6−i6i6−i6−i6i60000000000000000000000000000
χ654-4-444-4-2-444-422-244-4-4-224-42-2-2222-2-20000-22000000000000000000000000000000000000
χ664-4-44-44-244-4-422-200002-200-2-2220000−2i22i22i2−2i200i2−i2i2−i2−i2i2−i2i20000000000000000000000000000
χ674-4-44-44-244-4-422-200002-200-2-22200002i2−2i2−2i22i200−i2i2−i2i2i2−i2i2−i20000000000000000000000000000
χ684-4-44-44-2-4-44422-2-4-4442-24-422-2-2-2-2220000-22000000000000000000000000000000000000
χ6988-8-800-40000-44442−4242−4200000000−2222−2222000000000000000000000000000000000000000000
χ7088-8-800-40000-444−4242−42420000000022−2222−22000000000000000000000000000000000000000000
χ718-88-800-400004-4442−42−42420000000022−22−2222000000000000000000000000000000000000000000
χ728-88-800-400004-44−424242−4200000000−222222−22000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).