Finite Group DatabasebetaFinite Group Databasebeta| order | 31044 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C199⋊#261) |
| unambiguous semidirect product | C199⋊(C3⋊#261) |
| Fitting, socle, derived, Hall | C3×C13×C199 ⋊ C4 |
| Hall | C13×C199 ⋊ Dic3 |
| Hall | C3×C199 ⋊ #261 |
| Sylow | C199 ⋊ C3⋊#261 |
| Hall | C3×C13 ⋊ Dic199 |
| Sylow | C13 ⋊ Dic597 |
| Sylow | C3 ⋊ C199⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C13×C199 | C4 |
| prime radical, cosocle | C3×D13×C199 | C2 |
| LCS | G ▷ C3×C13×C199 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7761 |
Polycyclic presentation:
2^2,3,13,199|a^2=b,c^a=c^2,d^a=d^5,e^a=e^198,d^b=d^122391 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31044, 55);