Finite Group DatabasebetaFinite Group Databasebeta| order | 16317 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C72×C37 ⋊ C9 |
| Sylow | C72 ⋊ #66526 |
| Sylow | C37 ⋊ #89204 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C37 | C9 |
| prime radical, cosocle | C72×C37⋊C3 | C3 |
| LCS | G ▷ C72×C37 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1813 |
Polycyclic presentation:
3^2,7^2,37|a^3=b^2,c^a=c^2,d^a=d^2,e^a=e^34,e^b=e^26253 conjugacy classes — view the full character table.
| maximal subgroup of | #45657451, #45657454, #45657456, … |
| maximal normal subgroup of | #45657451, #45657454, #45657456, … |
| maximal quotient of | C2×#30654580 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16317, 31);