Finite Group DatabasebetaFinite Group Databasebeta| order | 32896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #398×C257 ⋊ C2 |
| Sylow | C257 ⋊ #2395 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D257 |
| commutator, socle, cosocle | C23×C257 | C24 |
| Fitting | #398×C257 | C2 |
| prime radical | C22×D1028 | C22 |
| hypercenter | #398 | D257 |
| hypocenter | C257 | #2395 |
| LCS | G ▷ C23×C257 ▷ C257 | |
| UCS | C1 ◁ C23 ◁ #398 | |
560 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 16448 |
Polycyclic presentation:
2^7,257|b^2=f,d^2=e,b^a=be,c^a=cf,h^a=h^256,c^b=cg,h^c=h^256,h^d=h^2562860 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32896, 7774);