Finite Group DatabasebetaFinite Group Databasebeta| order | 18876 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C3⋊(C11⋊(C11⋊#261)) |
| unambiguous semidirect product | C11⋊(C3⋊(C11⋊#261)) |
| Fitting, socle, derived, Hall | C3×C112×C13 ⋊ C4 |
| Hall | C112×C13 ⋊ Dic3 |
| Hall | C3×C112 ⋊ #261 |
| Sylow | C112 ⋊ C3⋊#261 |
| Hall | C3×C13 ⋊ C11⋊Dic11 |
| Sylow | C13 ⋊ C3⋊(C11⋊Dic11) |
| Sylow | C3 ⋊ C11⋊(C11⋊#261) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C112×C13 | C4 |
| prime radical, cosocle | C3×C112×D13 | C2 |
| LCS | G ▷ C3×C112×C13 | |
| UCS | C1 | |
168 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4719 |
Polycyclic presentation:
2^2,3,11^2,13|a^2=b,c^a=c^2,d^a=d^10,e^a=e^10,f^a=f^5,f^b=f^121455 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18876, 134);