Finite Group DatabasebetaFinite Group Databasebeta| order | 1092 |
| isoclinism | isoclinic class of D7×D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D7×D13 |
| Fitting, socle, Hall | C3×C7×C13 ⋊ C22 |
| derived, Hall | C7×C13 ⋊ C22×C3 |
| Hall | C3×C13 ⋊ C2×D7 |
| Hall | C3×C7 ⋊ C2×D13 |
| Sylow | C13 ⋊ C2×C3×D7 |
| Sylow | C7 ⋊ C2×C3×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D7×D13 |
| commutator, cosocle, hypocenter | C7×C13 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C13 | C22 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C3 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 273 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | D7×D13⋊C9, D13×D7⋊C9, #13109897⋊C2, … |
| maximal normal subgroup of | D7×D13⋊C9, D13×D7⋊C9, #13109897⋊C2, … |
| maximal quotient of | C9×D7×D13, C32×D7×D13, C3×D13×D21, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1092, 54);