Finite Group DatabasebetaFinite Group Databasebeta| order | 26450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×C5⋊(C23⋊D23) |
| unambiguous semidirect product | C5⋊(C5×C23⋊D23) |
| unambiguous semidirect product | C23⋊(C5×D115) |
| Fitting, socle, Hall | C52×C232 ⋊ C2 |
| derived | C5×C232 ⋊ C2×C5 |
| Sylow | C232 ⋊ C5×D5 |
| Sylow | C52 ⋊ C23⋊D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C5⋊(C23⋊D23) |
| commutator, cosocle, hypocenter | C5×C232 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C232 | C2 |
| LCS | G ▷ C5×C232 | |
| UCS | C1 ◁ C5 | |
260 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5290 |
6620 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26450, 22);