Finite Group DatabasebetaFinite Group Databasebeta| order | 18876 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | Dic13⋊(C112⋊C3) |
| derived, Hall | C112×C13 ⋊ C3×C4 |
| Hall | C112×Dic13 ⋊ C3 |
| Hall | C13⋊(C112⋊C3) ⋊ C4 |
| Sylow | C112 ⋊ Dic13⋊C3 |
| Hall | Dic13 ⋊ C112⋊C3 |
| Sylow | C13 ⋊ C4×C112⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D13⋊(C112⋊C3) |
| commutator, hypocenter | C112×C13 | C3×C4 |
| Fitting, socle, cosocle | C2×C112×C13 | C2×C3 |
| prime radical | C2×C13⋊(C112⋊C3) | C2 |
| LCS | G ▷ C112×C13 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1716 |
Polycyclic presentation:
2,3,11^2,13,2|a^2=f,e^a=e^12,c^b=c^3d^9,d^b=cd^7,e^b=e^3656 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18876, 53);