Finite Group DatabasebetaFinite Group Databasebeta| order | 36244 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C17×C41 ⋊ C4 |
| Hall | C17×C41 ⋊ #261 |
| Hall | C13×C41 ⋊ #595 |
| Hall | C13×C17 ⋊ #4223 |
| Sylow | C41 ⋊ #11725131 |
| Sylow | C17 ⋊ #14523822 |
| Sylow | C13 ⋊ #14584032 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C17×C41 | C4 |
| prime radical, cosocle | D9061 | C2 |
| LCS | G ▷ C13×C17×C41 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9061 |
Polycyclic presentation:
2^2,13,17,41|a^2=b,c^a=c^5,d^a=d^4,e^a=e^9,c^b=c^12,d^b=d^16,e^b=e^402269 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36244, 27);