Finite Group DatabasebetaFinite Group Databasebeta| order | 16428 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C372 ⋊ C3×C4 |
| Hall | #19129960 ⋊ C3 |
| Hall | #16861552 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C372 | C3×C4 |
| prime radical | #22551387 | C2 |
| cosocle | C37×D37 | C2×C3 |
| LCS | G ▷ C372 | |
| UCS | C1 | |
27 conjugacy classes of subgroups.
| transitive degree | μt(G) = 444 |
Polycyclic presentation:
2,3,2,37^2|a^2=c,d^a=d^31,e^a=e^36,d^b=d^26,e^b=e^10,d^c=d^36135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16428, 51);