Finite Group DatabasebetaFinite Group Databasebeta| order | 30492 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×C7×#10624391 |
| Fitting, socle | C2×C3×C7×C112 ⋊ D3 |
| derived | C112⋊C3 ⋊ C22×C3×C7 |
| Hall | C3×C7×C112⋊C3 ⋊ C22 |
| Hall | C3×C112⋊C3 ⋊ C22×C7 |
| Hall | C7×C112 ⋊ C2×C3×D3 |
| Sylow | C112 ⋊ C2×C3×D3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C7 | #10624391 |
| commutator, cosocle, hypocenter | C112⋊C3 | C22×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C7×C112 | D3 |
| LCS | G ▷ C112⋊C3 | |
| UCS | C1 ◁ C2×C3×C7 | |
136 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1386 |
1596 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30492, 365);