Finite Group DatabasebetaFinite Group Databasebeta| order | 26510 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D241⋊C5 |
| unambiguous semidirect product | D241⋊(C5×C11) |
| unambiguous semidirect product | (C241⋊C5)⋊(C2×C11) |
| Fitting, socle, Hall | C11×C241 ⋊ C2×C5 |
| derived, Sylow | C241 ⋊ C2×C5×C11 |
| Hall | C11×C241⋊C5 ⋊ C2 |
| Hall | C11×D241 ⋊ C5 |
| Hall | C241⋊C5 ⋊ C2×C11 |
| Hall | D241 ⋊ C5×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D241⋊C5 |
| commutator, cosocle, hypocenter | C241 | C2×C5×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C241 | C2×C5 |
| LCS | G ▷ C241 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2651 |
374 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26510, 15);