Finite Group DatabasebetaFinite Group Databasebeta| order | 3612 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D7×D43 |
| Fitting, socle, Hall | C3×C7×C43 ⋊ C22 |
| derived, Hall | C7×C43 ⋊ C22×C3 |
| Hall | C3×C43 ⋊ C2×D7 |
| Sylow | C43 ⋊ C2×C3×D7 |
| Hall | C3×C7 ⋊ C2×D43 |
| Sylow | C7 ⋊ C2×C3×D43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D7×D43 |
| commutator, cosocle, hypocenter | C7×C43 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C43 | C22 |
| LCS | G ▷ C7×C43 | |
| UCS | C1 ◁ C3 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 903 |
345 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #19129334⋊C2, #19129333⋊C2, D43×D7⋊C9, … |
| maximal normal subgroup of | #19129334⋊C2, #19129333⋊C2, D43×D7⋊C9, … |
| maximal quotient of | C9×D7×D43, C32×D7×D43, C3×D21×D43, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3612, 57);