Finite Group DatabasebetaFinite Group Databasebeta| order | 26124 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C311 · Schur multiplier (H2) = C2 |
| Fitting, socle, Hall | C22×C7×C311 ⋊ C3 |
| derived, Hall | C22×C7 ⋊ C3×C311 |
| Hall | C7×C311 ⋊ A4 |
| Hall | C22×C311 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ A4×C311 |
| Sylow | C22 ⋊ ΓL(1,𝔽8)×C311 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C311 | C22⋊ΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C22×C7 | C3×C311 |
| Frattini | C1 | G |
| Fitting, socle | C22×C7×C311 | C3 |
| LCS | G ▷ C22×C7 | |
| UCS | C1 ◁ C311 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8708 |
3732 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26124, 26);