Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C31×#120 ⋊ C2 |
| Sylow | C31 ⋊ #2404 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D31 |
| commutator, socle, cosocle | C23×C31 | C24 |
| Fitting | C2×C31×#120 | C2 |
| hypercenter | C2×#120 | D31 |
| hypocenter | C31 | #2404 |
| LCS | G ▷ C23×C31 ▷ C31 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
1056 conjugacy classes of subgroups.
| transitive degree | μt(G) = 992 |
Polycyclic presentation:
2^7,31|b^2=e,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^30458 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 7826);