Finite Group DatabasebetaFinite Group Databasebeta| order | 26950 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C7 |
| direct product | C11×C7⋊D175 |
| unambiguous semidirect product | C7⋊(C11×D175) |
| unambiguous semidirect product | C25⋊(C11×C7⋊D7) |
| Fitting, Hall | C72×C11×C25 ⋊ C2 |
| derived, Hall | C72×C25 ⋊ C2×C11 |
| Hall | C72×C11 ⋊ D25 |
| Hall | C11×C25 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ C11×D25 |
| Sylow | C25 ⋊ C11×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C7⋊D175 |
| commutator, cosocle, hypocenter | C72×C25 | C2×C11 |
| Frattini | C5 | C11×C5⋊(C7⋊D7) |
| Fitting | C72×C11×C25 | C2 |
| socle | C5×C72×C11 | D5 |
| LCS | G ▷ C72×C25 | |
| UCS | C1 ◁ C11 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13475 |
6754 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26950, 49);