Finite Group DatabasebetaFinite Group Databasebeta| order | 3906 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C31 ⋊ C2×C9 |
| Hall | #14519870 ⋊ C2 |
| Hall | C7×D31 ⋊ C9 |
| Hall | D31 ⋊ C7⋊C9 |
| Sylow | C31 ⋊ C2×C7⋊C9 |
| Sylow | C7 ⋊ D31⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #13049955 |
| commutator, hypocenter | C7×C31 | C2×C9 |
| Fitting, socle, cosocle | C3×C7×C31 | C2×C3 |
| prime radical | C3×C7×D31 | C3 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1953 |
Polycyclic presentation:
2,3,7,31,3|b^3=e,d^a=d^30,c^b=c^4,d^b=d^5135 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#16840857, C5⋊#16840857, #16840857⋊C5, … |
| maximal normal subgroup of | C5×#16840857, #16840857⋊C5, C7×#16840857 |
| maximal quotient of | C5×#16840857, C5⋊#16840857, #41032301, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3906, 7);