Finite Group DatabasebetaFinite Group Databasebeta| order | 24642 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C372 ⋊ C2×C9 |
| Hall | #27134469 ⋊ C2 |
| Hall | C37⋊D37 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C372 | C2×C9 |
| prime radical | #22551388 | C3 |
| cosocle | #16861552 | C2×C3 |
| LCS | G ▷ C372 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 333 |
Polycyclic presentation:
2,3^2,37^2|b^3=c,d^a=d^36,e^a=e^36,d^b=d^16,e^b=e^34,d^c=d^26,e^c=e^1094 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24642, 56);