Finite Group DatabasebetaFinite Group Databasebeta| order | 29796 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C191⋊#261) |
| unambiguous semidirect product | C191⋊(C3⋊#261) |
| Fitting, socle, derived, Hall | C3×C13×C191 ⋊ C4 |
| Hall | C13×C191 ⋊ Dic3 |
| Hall | C3×C191 ⋊ #261 |
| Sylow | C191 ⋊ C3⋊#261 |
| Hall | C3×C13 ⋊ Dic191 |
| Sylow | C13 ⋊ Dic573 |
| Sylow | C3 ⋊ C191⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C13×C191 | C4 |
| prime radical, cosocle | C3×D13×C191 | C2 |
| LCS | G ▷ C3×C13×C191 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7449 |
Polycyclic presentation:
2^2,3,13,191|a^2=b,c^a=c^2,d^a=d^5,e^a=e^190,d^b=d^122295 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29796, 25);