Finite Group DatabasebetaFinite Group Databasebeta| order | 3612 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic301 |
| derived, Hall | C7×C43 ⋊ C3×C4 |
| Hall | C3×C7×C43 ⋊ C4 |
| Hall | C3×C43 ⋊ Dic7 |
| Sylow | C43 ⋊ C3×Dic7 |
| Hall | C3×C7 ⋊ Dic43 |
| Sylow | C7 ⋊ C3×Dic43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D301 |
| commutator, hypocenter | C7×C43 | C3×C4 |
| Frattini | C2 | C3×D301 |
| Fitting, socle, prime radical | C2×C3×C7×C43 | C2 |
| cosocle | C2×C7×C43 | C2×C3 |
| LCS | G ▷ C7×C43 | |
| UCS | C1 ◁ C2×C3 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 3612 |
912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C43⋊C9)⋊Dic7, (C7⋊C9)⋊Dic43, #24925426, … |
| maximal normal subgroup of | (C43⋊C9)⋊Dic7, (C7⋊C9)⋊Dic43, #24925426, … |
| maximal quotient of | C9×Dic301, C32×Dic301, C3×Dic903, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3612, 26);