Finite Group DatabasebetaFinite Group Databasebeta| order | 30492 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D21×#10624391 |
| Fitting, socle | C3×C7×C112 ⋊ C2×D3 |
| derived, Hall | C3×C7×C112⋊C3 ⋊ C22 |
| Hall | C3×C112⋊C3 ⋊ C2×D7 |
| Hall | C7×C112 ⋊ D32 |
| Sylow | C112 ⋊ D3×D21 |
| Sylow | C7 ⋊ D3×#10624391 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C7×C112⋊C3 | C22 |
| Fitting, socle | C3×C7×C112 | C2×D3 |
| LCS | G ▷ C3×C7×C112⋊C3 | |
| UCS | C1 | |
136 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 21 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 693 |
456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30492, 342);