Finite Group DatabasebetaFinite Group Databasebeta| order | 15717 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C31×C169 ⋊ C3 |
| Sylow | C169 ⋊ C31⋊C3 |
| Sylow | C31 ⋊ C169⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C31×C169 | C3 |
| Frattini | C13 | #11925881 |
| socle | C13×C31 | C13⋊C3 |
| LCS | G ▷ C31×C169 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5239 |
Polycyclic presentation:
3,13,31,13|b^13=d^6,b^a=b^3d,c^a=c^5,d^a=d^31749 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#30628398, #44537619, #44537623, … |
| maximal normal subgroup of | C2×#30628398, #44537619, #44537623, … |
| maximal quotient of | C2×#30628398 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15717, 4);