Finite Group DatabasebetaFinite Group Databasebeta| order | 32464 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D4×C2029 ⋊ C2 |
| Sylow | C2029 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D2029 |
| commutator, cosocle | C4×C2029 | C22 |
| Frattini | C4 | C2×D2029 |
| Fitting | D4×C2029 | C2 |
| socle | C2×C2029 | D4 |
| hypercenter | D4 | D2029 |
| hypocenter | C2029 | D8 |
| LCS | G ▷ C4×C2029 ▷ C2×C2029 ▷ C2029 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16232 |
Polycyclic presentation:
2^4,2029|c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^20285077 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32464, 25);