Finite Group DatabasebetaFinite Group Databasebeta| order | 26901 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| Fitting, derived, Hall | C49×C61 ⋊ C32 |
| Sylow | C61 ⋊ C3×C49⋊C3 |
| Sylow | C49 ⋊ C3×C61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C49×C61 | C32 |
| Frattini | C7 | ΓL(1,𝔽8)×C61⋊C3 |
| socle | C7×C61 | C3×ΓL(1,𝔽8) |
| LCS | G ▷ C49×C61 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2989 |
437 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26901, 7);