Finite Group DatabasebetaFinite Group Databasebeta| order | 26150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×D523 |
| unambiguous semidirect product | C523⋊(C2×C52) |
| Fitting, socle, Hall | C52×C523 ⋊ C2 |
| derived, Sylow | C523 ⋊ C2×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D523 |
| commutator, cosocle, hypocenter | C523 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C523 | C2 |
| LCS | G ▷ C523 | |
| UCS | C1 ◁ C52 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13075 |
6575 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26150, 6);