Finite Group DatabasebetaFinite Group Databasebeta| order | 25012 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C169 · Schur multiplier (H2) = C1 |
| direct product | Dic37×C169 |
| derived, Sylow | C37 ⋊ C4×C169 |
| Hall | C37×C169 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C169 | D37 |
| commutator, hypocenter | C37 | C4×C169 |
| Frattini | C2×C13 | C13×D37 |
| Fitting | C2×C37×C169 | C2 |
| socle, prime radical, cosocle | C2×C13×C37 | C2×C13 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C2×C169 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 25012 |
6760 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25012, 3);