Finite Group DatabasebetaFinite Group Databasebeta| order | 18876 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #10624391⋊D13 |
| Fitting, socle, Hall | C112×C13 ⋊ C2×D3 |
| derived, Hall | C13×C112⋊C3 ⋊ C22 |
| Hall | C112⋊C3 ⋊ C2×D13 |
| Sylow | C112 ⋊ D3×D13 |
| Sylow | C13 ⋊ #10624391⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C13×C112⋊C3 | C22 |
| Fitting, socle | C112×C13 | C2×D3 |
| LCS | G ▷ C13×C112⋊C3 | |
| UCS | C1 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 429 |
Polycyclic presentation:
2^2,3,13,11^2|d^a=d^12,e^a=e^10,f^a=f^10,c^b=c^2,e^b=e^3f^10,f^b=e^8f^8,e^c=e^2f^10,f^c=e^7f^8259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18876, 79);