Finite Group DatabasebetaFinite Group Databasebeta| order | 24642 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | (C37⋊C3)⋊(D37⋊C3) |
| unambiguous semidirect product | ((C37⋊C3)⋊D37)⋊C3 |
| unambiguous semidirect product | #22551385⋊C3 |
| unambiguous semidirect product | #22551388⋊C3 |
| Fitting, socle, derived, Sylow | C372 ⋊ C2×C32 |
| Hall | C37⋊C32 ⋊ C2 |
| Hall | C37⋊D37 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C372 | C2×C32 |
| LCS | G ▷ C372 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 111 |
Polycyclic presentation:
2,3^2,37^2|d^a=d^36,e^a=e^36,d^b=d^26,e^c=e^26126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24642, 46);