Finite Group DatabasebetaFinite Group Databasebeta| order | 26901 |
| automorphism | ? |
| homology | Abelianization (H1) = C72×C9 · Schur multiplier (H2) = C7 |
| direct product | C72×C61⋊C9 |
| unambiguous semidirect product | C61⋊(C72×C9) |
| derived, Sylow | C61 ⋊ C72×C9 |
| Hall | C72×C61 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C72 | C61⋊C3 |
| commutator, hypocenter | C61 | C72×C9 |
| Frattini | C3 | C72×C61⋊C3 |
| Fitting, socle, prime radical | C3×C72×C61 | C3 |
| cosocle | C3×C61 | C3×C72 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C3×C72 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 26901 |
3381 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26901, 21);