Finite Group DatabasebetaFinite Group Databasebeta| order | 24642 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C372 ⋊ C2×C9 |
| Hall | #27134460 ⋊ C2 |
| Hall | C37⋊D37 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #22551385 |
| commutator, hypocenter | C372 | C2×C9 |
| Fitting, socle, cosocle | C3×C372 | C2×C3 |
| prime radical | C3×C37⋊D37 | C3 |
| LCS | G ▷ C372 | |
| UCS | C1 ◁ C3 | |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12321 |
Polycyclic presentation:
2,3,37^2,3|b^3=e,c^a=c^36,d^a=d^36,c^b=c^26,d^b=d^26702 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24642, 24);