Finite Group DatabasebetaFinite Group Databasebeta| order | 26901 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C61 · Schur multiplier (H2) = C3 |
| direct product | C3×C61×C49⋊C3 |
| unambiguous semidirect product | C49⋊(C32×C61) |
| unambiguous semidirect product | (C3×C49)⋊(C3×C61) |
| Fitting | C3×C49×C61 ⋊ C3 |
| derived, Sylow | C49 ⋊ C32×C61 |
| Hall | C49×C61 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C61 | C49⋊C3 |
| commutator, cosocle, hypocenter | C49 | C32×C61 |
| Frattini | C7 | C3×ΓL(1,𝔽8)×C61 |
| Fitting | C3×C49×C61 | C3 |
| socle | C3×C7×C61 | ΓL(1,𝔽8) |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C3×C61 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8967 |
3477 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26901, 10);