Finite Group DatabasebetaFinite Group Databasebeta| order | 3906 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D651 |
| unambiguous semidirect product | C7⋊(C3⋊D93) |
| unambiguous semidirect product | C31⋊(C3⋊D21) |
| Fitting, socle, derived, Hall | C32×C7×C31 ⋊ C2 |
| Hall | C32×C31 ⋊ D7 |
| Hall | C7×C31 ⋊ C3⋊D3 |
| Hall | C32×C7 ⋊ D31 |
| Sylow | C31 ⋊ C3⋊D21 |
| Sylow | C32 ⋊ D217 |
| Sylow | C7 ⋊ C3⋊D93 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C7×C31 | C2 |
| LCS | G ▷ C32×C7×C31 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1953 |
Polycyclic presentation:
2,3^2,7,31|b^a=b^2,c^a=c^2,d^a=d^6,e^a=e^30978 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊(C3⋊(C7⋊(D31⋊C5))), C3⋊D3255, C5×C3⋊D651, … |
| maximal normal subgroup of | C3⋊(C3⋊(C7⋊(D31⋊C5))), C5×C3⋊D651, C7×C3⋊D651 |
| maximal quotient of | C3⋊D3255, C5×C3⋊D651, C3⋊D4557, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3906, 72);