Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C31 ⋊ #2378 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D31 |
| commutator | C22×C31 | C23×C4 |
| Fitting | C31×#381 | C2 |
| socle, cosocle | C23×C31 | C24 |
| prime radical | C24×C31 | C23 |
| hypercenter | #381 | D31 |
| hypocenter | C31 | #2378 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C23 ◁ #381 | |
464 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1984 |
Polycyclic presentation:
2^7,31|a^2=g,b^2=e,d^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^30,c^b=cef,d^b=de,h^b=h^30458 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 7678);