Finite Group DatabasebetaFinite Group Databasebeta| order | 26052 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C167⋊#261) |
| unambiguous semidirect product | C167⋊(C3⋊#261) |
| Fitting, socle, derived, Hall | C3×C13×C167 ⋊ C4 |
| Hall | C13×C167 ⋊ Dic3 |
| Hall | C3×C167 ⋊ #261 |
| Sylow | C167 ⋊ C3⋊#261 |
| Hall | C3×C13 ⋊ Dic167 |
| Sylow | C13 ⋊ Dic501 |
| Sylow | C3 ⋊ C167⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C13×C167 | C4 |
| prime radical, cosocle | C3×D13×C167 | C2 |
| LCS | G ▷ C3×C13×C167 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6513 |
Polycyclic presentation:
2^2,3,13,167|a^2=b,c^a=c^2,d^a=d^5,e^a=e^166,d^b=d^122007 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26052, 25);