Finite Group DatabasebetaFinite Group Databasebeta| order | 37539 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C43×C97 ⋊ C9 |
| Sylow | C97 ⋊ C43⋊C9 |
| Sylow | C43 ⋊ C97⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #27159830 |
| commutator, hypocenter | C43×C97 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C43×C97 | C3 |
| LCS | G ▷ C43×C97 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 37539 |
Polycyclic presentation:
3,43,97,3|a^3=d,b^a=b^36,c^a=c^354179 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37539, 5);