Finite Group DatabasebetaFinite Group Databasebeta| order | 18876 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C13×C112⋊C3 ⋊ C4 |
| Hall | C112×C13 ⋊ Dic3 |
| Hall | C112⋊C3 ⋊ Dic13 |
| Sylow | C112 ⋊ Dic39 |
| Sylow | C13 ⋊ #13089712 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C13⋊#10624391 |
| commutator, hypocenter | C13×C112⋊C3 | C4 |
| Fitting, socle | C2×C112×C13 | D3 |
| prime radical, cosocle | C2×C13×C112⋊C3 | C2 |
| LCS | G ▷ C13×C112⋊C3 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1716 |
Polycyclic presentation:
2,3,13,11^2,2|a^2=f,b^a=b^2,c^a=c^12,d^a=d^2e^10,e^a=d^3e^9,d^b=d^2e^10,e^b=d^7e^8592 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18876, 48);