Finite Group DatabasebetaFinite Group Databasebeta| order | 32288 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×D4×C1009 ⋊ C2 |
| Sylow | C1009 ⋊ #120 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D1009 |
| commutator, socle, cosocle | C22×C1009 | C23 |
| Fitting | C2×D4×C1009 | C2 |
| hypercenter | C2×D4 | D1009 |
| hypocenter | C1009 | #120 |
| LCS | G ▷ C22×C1009 ▷ C1009 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8072 |
Polycyclic presentation:
2^5,1009|b^a=bd,c^a=ce,f^c=f^10085054 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32288, 114);