Finite Group DatabasebetaFinite Group Databasebeta| order | 32301 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C37×C97 ⋊ C9 |
| Sylow | C97 ⋊ #66524 |
| Sylow | C37 ⋊ C97⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #24924601 |
| commutator, hypocenter | C37×C97 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C37×C97 | C3 |
| LCS | G ▷ C37×C97 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32301 |
Polycyclic presentation:
3,37,97,3|a^3=d,b^a=b^10,c^a=c^353597 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32301, 4);