Finite Group DatabasebetaFinite Group Databasebeta| order | 3844 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C31 |
| unambiguous semidirect product | C31⋊Dic31 |
| derived, Sylow | C312 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C31⋊D31 |
| commutator, hypocenter | C312 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C312 | C2 |
| LCS | G ▷ C312 | |
| UCS | C1 ◁ C2 | |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3844 |
Polycyclic presentation:
2,31^2,2|a^2=d,b^a=b^30,c^a=c^30964 conjugacy classes — view the full character table.
| maximal subgroup of | #26040335, #26040336, (C31⋊C3)⋊Dic31, … |
| maximal normal subgroup of | #26040335, #26040336, (C31⋊C3)⋊Dic31, … |
| maximal quotient of | C3×C31⋊Dic31, C3⋊(C31⋊Dic31), C5×C31⋊Dic31, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3844, 7);