Finite Group DatabasebetaFinite Group Databasebeta| order | 30492 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×D11×D77 |
| unambiguous semidirect product | (C11×D11)⋊(C9×D7) |
| Fitting, Hall | C7×C9×C112 ⋊ C22 |
| derived, Hall | C7×C112 ⋊ C22×C9 |
| Hall | C9×C112 ⋊ C2×D7 |
| Sylow | C112 ⋊ C2×C9×D7 |
| Hall | C7×C9 ⋊ D112 |
| Sylow | C7 ⋊ C9×D112 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D11×D77 |
| commutator, hypocenter | C7×C112 | C22×C9 |
| Frattini | C3 | C3×D11×D77 |
| Fitting | C7×C9×C112 | C22 |
| socle, cosocle | C3×C7×C112 | C22×C3 |
| prime radical | C3×D11×D77 | C3 |
| LCS | G ▷ C7×C112 | |
| UCS | C1 ◁ C9 | |
180 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1386 |
2520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30492, 177);