Finite Group DatabasebetaFinite Group Databasebeta| order | 31332 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C373 ⋊ C3×C4 |
| Hall | C7×#13093637 ⋊ C3 |
| Hall | #21463180 ⋊ C4 |
| Hall | #13093637 ⋊ ΓL(1,𝔽8) |
| Sylow | C373 ⋊ C4×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ #13093637⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C373 | C3×C4 |
| prime radical | #30627834 | C2 |
| cosocle | C7×D373 | C2×C3 |
| LCS | G ▷ C7×C373 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2611 |
Polycyclic presentation:
2,3,2,7,373|a^2=c,e^a=e^104,d^b=d^2,e^b=e^284,e^c=e^372237 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31332, 33);