Finite Group DatabasebetaFinite Group Databasebeta| order | 32288 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C1009 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D1009 |
| commutator, socle | C2×C1009 | C22×C4 |
| Fitting, prime radical | #41×C1009 | C2 |
| cosocle | C4×C1009 | C23 |
| hypercenter | #41 | D1009 |
| hypocenter | C1009 | #131 |
| LCS | G ▷ C2×C1009 ▷ C1009 | |
| UCS | C1 ◁ C4 ◁ #41 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16144 |
Polycyclic presentation:
2^5,1009|a^2=d,d^2=e,f^a=f^1008,c^b=ce5060 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32288, 153);