Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Sylow | C31 ⋊ #2308 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D31 |
| commutator | C22×C31 | C23×C4 |
| Fitting, prime radical | C23×D4×C31 | C2 |
| socle, cosocle | C23×C31 | C24 |
| hypercenter | C23×D4 | D31 |
| hypocenter | C31 | #2308 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
1160 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 309 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 992 |
Polycyclic presentation:
2^7,31|a^2=g,b^a=be,c^a=cf,d^a=de,h^a=h^30,c^b=ce644 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 7088);