Finite Group DatabasebetaFinite Group Databasebeta| order | 26733 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C67 · Schur multiplier (H2) = C1 |
| direct product | C67×#87704 |
| Fitting, socle, Hall | C7×C19×C67 ⋊ C3 |
| derived, Hall | C7×C19 ⋊ C3×C67 |
| Hall | C19×C67 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C67 ⋊ C19⋊C3 |
| Sylow | C19 ⋊ ΓL(1,𝔽8)×C67 |
| Sylow | C7 ⋊ C19⋊C3×C67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C67 | #87704 |
| commutator, cosocle, hypocenter | C7×C19 | C3×C67 |
| Frattini | C1 | G |
| Fitting, socle | C7×C19×C67 | C3 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 ◁ C67 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8911 |
3149 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26733, 9);