Finite Group DatabasebetaFinite Group Databasebeta| order | 32272 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C8×C2017 ⋊ C2 |
| Sylow | C2017 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D2017 |
| commutator, socle | C2×C2017 | C2×C4 |
| Fitting | C8×C2017 | C2 |
| prime radical | C2×D2017 | C4 |
| cosocle | C4×C2017 | C22 |
| hypercenter | C8 | D2017 |
| hypocenter | C2017 | M16 |
| LCS | G ▷ C2×C2017 ▷ C2017 | |
| UCS | C1 ◁ C4 ◁ C8 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16136 |
Polycyclic presentation:
2^4,2017|a^2=c,c^2=d,b^a=bd,e^b=e^20168074 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32272, 23);