Finite Group DatabasebetaFinite Group Databasebeta| order | 26862 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | D37⋊(C112⋊C3) |
| Fitting, socle, derived, Hall | C112×C37 ⋊ C2×C3 |
| Hall | C37⋊(C112⋊C3) ⋊ C2 |
| Hall | C112×D37 ⋊ C3 |
| Sylow | C112 ⋊ D37⋊C3 |
| Hall | D37 ⋊ C112⋊C3 |
| Sylow | C37 ⋊ C2×C112⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C37 | C2×C3 |
| LCS | G ▷ C112×C37 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1221 |
Polycyclic presentation:
2,3,11^2,37|e^a=e^36,c^b=c^6d^6,d^b=c^2d^4,e^b=e^26812 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26862, 14);