Finite Group DatabasebetaFinite Group Databasebeta| order | 3822 |
| isoclinism | isoclinic class of D91 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×D91 |
| Fitting, socle, Hall | C3×C72×C13 ⋊ C2 |
| derived | C7×C13 ⋊ C2×C3×C7 |
| Hall | C72×C13 ⋊ C2×C3 |
| Hall | C3×C72 ⋊ D13 |
| Sylow | C72 ⋊ C3×D13 |
| Hall | C3×C13 ⋊ C7×D7 |
| Sylow | C13 ⋊ C3×C7×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | D91 |
| commutator, cosocle, hypocenter | C7×C13 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C13 | C2 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C3×C7 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 546 |
987 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×#13109902, C7×#13109903, C7×(C7⋊C9)⋊D13, … |
| maximal normal subgroup of | C7×#13109902, C7×#13109903, C7×(C7⋊C9)⋊D13, … |
| maximal quotient of | C7×C9×D91, C3×C7×D273, C32×C7×D91, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3822, 92);