Finite Group DatabasebetaFinite Group Databasebeta| order | 31542 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C751 ⋊ C2×C3 |
| Hall | #30628831 ⋊ C2 |
| Hall | D7×C751 ⋊ C3 |
| Sylow | C751 ⋊ AGL(1,𝔽7) |
| Hall | D7 ⋊ C751⋊C3 |
| Sylow | C7 ⋊ C2×C751⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C751 | C2×C3 |
| LCS | G ▷ C7×C751 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5257 |
Polycyclic presentation:
2,3,7,751|c^a=c^6,c^b=c^2,d^b=d^6781257 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31542, 19);