Finite Group DatabasebetaFinite Group Databasebeta| order | 3844 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C31 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C312 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C312 | C4 |
| prime radical, cosocle | C31⋊D31 | C2 |
| LCS | G ▷ C312 | |
| UCS | C1 | |
38 conjugacy classes of subgroups.
| minimal degree | μ(G) = 62 |
| transitive degree | μt(G) = 62 |
Polycyclic presentation:
2^2,31^2|a^2=b,c^a=c^27d^4,d^a=c^19d^4,c^b=c^30,d^b=d^30244 conjugacy classes — view the full character table.
| maximal subgroup of | #26040355, #16838652⋊C3, C3×#16838652, … |
| maximal normal subgroup of | #16838652⋊C3, C3×#16838652, #16838652⋊C5, … |
| maximal quotient of | C3×#16838652, C3⋊#16838652, C5×#16838652, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3844, 10);