Finite Group DatabasebetaFinite Group Databasebeta| order | 15717 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C132×C31 ⋊ C3 |
| Sylow | C132 ⋊ C31⋊C3 |
| Sylow | C31 ⋊ #92788 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C132×C31 | C3 |
| LCS | G ▷ C132×C31 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5239 |
Polycyclic presentation:
3,13^2,31|b^a=b^9,c^a=c^9,d^a=d^51749 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44537656, #44537660, #44537662, … |
| maximal normal subgroup of | #44537656, #44537660, #44537662, … |
| maximal quotient of | C2×#30628406 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15717, 12);