Finite Group DatabasebetaFinite Group Databasebeta| order | 32192 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #95×C503 ⋊ C2 |
| Sylow | C503 ⋊ #393 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D503 |
| commutator, socle, cosocle | C23×C503 | C23 |
| Fitting | #95×C503 | C2 |
| prime radical | C23×D503 | C22 |
| hypercenter | #95 | D503 |
| hypocenter | C503 | #393 |
| LCS | G ▷ C23×C503 ▷ C503 | |
| UCS | C1 ◁ C23 ◁ #95 | |
202 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 16096 |
Polycyclic presentation:
2^6,503|a^2=d,b^2=d,b^a=bd,c^a=ce,c^b=cf,g^b=g^502,g^c=g^5025042 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32192, 462);