Finite Group DatabasebetaFinite Group Databasebeta| order | 26862 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×#10624391 |
| Fitting, socle, Hall | C112×C37 ⋊ D3 |
| derived, Hall | C112⋊C3 ⋊ C2×C37 |
| Hall | C37×C112⋊C3 ⋊ C2 |
| Sylow | C112 ⋊ D3×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | #10624391 |
| commutator, cosocle, hypocenter | C112⋊C3 | C2×C37 |
| Frattini | C1 | G |
| Fitting, socle | C112×C37 | D3 |
| LCS | G ▷ C112⋊C3 | |
| UCS | C1 ◁ C37 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1221 |
1406 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26862, 16);