Finite Group DatabasebetaFinite Group Databasebeta| order | 16428 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #22551385⋊C2 |
| unambiguous semidirect product | #22551386⋊C2 |
| Fitting, socle, derived, Sylow | C372 ⋊ C22×C3 |
| Hall | D372 ⋊ C3 |
| Hall | #16861551 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C372 | C22×C3 |
| LCS | G ▷ C372 | |
| UCS | C1 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 74 |
Polycyclic presentation:
2^2,3,37^2|e^a=e^36,d^b=d^36,d^c=d^26,e^c=e^26144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16428, 54);