Finite Group DatabasebetaFinite Group Databasebeta| order | 25012 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C13 |
No aliases for this group.
| derived, Hall | C132×C37 ⋊ C4 |
| Sylow | C132 ⋊ Dic37 |
| Sylow | C37 ⋊ #10621725 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C13⋊D481 |
| commutator, hypocenter | C132×C37 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C132×C37 | C2 |
| LCS | G ▷ C132×C37 | |
| UCS | C1 ◁ C2 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 25012 |
Polycyclic presentation:
2,13^2,37,2|a^2=e,b^a=b^12,c^a=c^12,d^a=d^366256 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25012, 17);