Finite Group DatabasebetaFinite Group Databasebeta| order | 26450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C5 |
| direct product | C23×C5⋊D115 |
| unambiguous semidirect product | C5⋊(C23×D115) |
| unambiguous semidirect product | C23⋊(C23×C5⋊D5) |
| Fitting, socle, Hall | C52×C232 ⋊ C2 |
| derived | C52×C23 ⋊ C2×C23 |
| Sylow | C232 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ C23×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C5⋊D115 |
| commutator, cosocle, hypocenter | C52×C23 | C2×C23 |
| Frattini | C1 | G |
| Fitting, socle | C52×C232 | C2 |
| LCS | G ▷ C52×C23 | |
| UCS | C1 ◁ C23 | |
152 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1150 |
6647 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26450, 24);