Finite Group DatabasebetaFinite Group Databasebeta| order | 32708 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C17×C37 ⋊ C4 |
| Hall | C17×C37 ⋊ #261 |
| Hall | C13×C37 ⋊ #595 |
| Hall | C13×C17 ⋊ #3866 |
| Sylow | C37 ⋊ #11725131 |
| Sylow | C17 ⋊ #14515321 |
| Sylow | C13 ⋊ #14578980 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C17×C37 | C4 |
| prime radical, cosocle | D8177 | C2 |
| LCS | G ▷ C13×C17×C37 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8177 |
Polycyclic presentation:
2^2,13,17,37|a^2=b,c^a=c^5,d^a=d^4,e^a=e^31,c^b=c^12,d^b=d^16,e^b=e^362048 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32708, 26);