Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C13×#1579 ⋊ C2 |
| Sylow | C13 ⋊ #19762 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D4×D52 |
| commutator, cosocle | C42×C13 | C24 |
| Frattini | C42 | C23×D13 |
| Fitting | C13×#1579 | C2 |
| socle | C22×C13 | D42 |
| hypercenter | #1579 | D13 |
| hypocenter | C13 | #19762 |
| LCS | G ▷ C42×C13 ▷ C22×C13 ▷ C13 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #1579 | |
728 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1664 |
Polycyclic presentation:
2^8,13|b^2=g,c^2=g,d^2=g,e^2=g,f^2=h,b^a=be,c^a=cf,e^a=eg,f^a=fh,i^a=i^12,d^b=de,e^b=eg,f^c=fh,i^c=i^12,e^d=eg304 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 159022);