Finite Group DatabasebetaFinite Group Databasebeta| order | 32193 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C7 |
No aliases for this group.
| derived, Hall | C72×C73 ⋊ C9 |
| Sylow | C73 ⋊ #89205 |
| Sylow | C72 ⋊ #10620321 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C73⋊#3862 |
| commutator, hypocenter | C72×C73 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C72×C73 | C3 |
| LCS | G ▷ C72×C73 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4599 |
Polycyclic presentation:
3,7^2,73,3|a^3=e,b^a=b^4,c^a=c^2,d^a=d^83585 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32193, 16);