Finite Group DatabasebetaFinite Group Databasebeta| order | 32272 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C2017 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #22549029 |
| commutator, hypocenter | C2017 | C2×C8 |
| Frattini | C2 | C2×#22549029 |
| Fitting | C4×C2017 | C4 |
| socle | C2×C2017 | C2×C4 |
| prime radical | C2×D2017 | C4 |
| cosocle | Dic2017 | C22 |
| LCS | G ▷ C2017 | |
| UCS | C1 ◁ C4 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16136 |
Polycyclic presentation:
2^4,2017|a^2=c,c^2=d,e^a=e^229,e^b=e^2016,e^c=e^20162032 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32272, 48);