Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#11924246 |
| derived, Hall | C3×C72 ⋊ C22×C4 |
| Sylow | C72 ⋊ C2×C4×D3 |
| Sylow | C3 ⋊ C2×#87639 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D7×D21 |
| commutator, hypocenter | C3×C72 | C22×C4 |
| Frattini | C2 | C2×D7×D21 |
| Fitting, socle | C22×C3×C72 | C22 |
| prime radical | C22×C3⋊(C7⋊D7) | C2 |
| cosocle | C2×C3×C72 | C23 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C22 | |
312 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#87639, C2×#72222096, C2×#72222109, … |
| maximal normal subgroup of | C2×D3×#87639, C2×#72222096, C2×#72222109, … |
| maximal quotient of | #72254218 |
Past the SmallGroups library coverage — no SmallGroups id.