Finite Group DatabasebetaFinite Group Databasebeta| order | 26950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C72×C25 · Schur multiplier (H2) = C7 |
| direct product | C2×C72×C11⋊C25 |
| unambiguous semidirect product | (C2×C11)⋊(C72×C25) |
| unambiguous semidirect product | (C2×C7×C11)⋊(C7×C25) |
| unambiguous semidirect product | (C2×C72×C11)⋊C25 |
| derived, Sylow | C11 ⋊ C2×C72×C25 |
| Hall | C2×C72×C11 ⋊ C25 |
| Hall | C72×C11 ⋊ C2×C25 |
| Hall | C2×C11 ⋊ C72×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5×C72 | C11⋊C5 |
| commutator, hypocenter | C11 | C2×C72×C25 |
| Frattini | C5 | C2×C72×C11⋊C5 |
| Fitting, socle, prime radical | C2×C5×C72×C11 | C5 |
| cosocle | C5×C11 | C2×C5×C72 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C2×C5×C72 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 26950 |
3430 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26950, 39);