Finite Group DatabasebetaFinite Group Databasebeta| order | 24642 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | #27134461 ⋊ C2 |
| Sylow | C372 ⋊ D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #27134461 | C2 |
| Frattini | C3 | #22551381 |
| Fitting, socle | C3×C372 | D3 |
| LCS | G ▷ #27134461 | |
| UCS | C1 | |
33 conjugacy classes of subgroups.
| transitive degree | μt(G) = 333 |
Polycyclic presentation:
2,3,37^2,3|b^3=e^2,b^a=b^2e,c^a=d,d^a=c,e^a=e^2,c^b=c^26,d^b=d^10744 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24642, 20);