Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#11924249 |
| Hall | C3×C72 ⋊ C2×D4 |
| Sylow | C72 ⋊ C2×#67 |
| Sylow | C3 ⋊ C2×#87641 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D7×D21 |
| commutator, cosocle | C2×C3×C72 | C23 |
| Frattini | C2 | C2×D7×D21 |
| Fitting, socle | C22×C3×C72 | C22 |
| hypocenter | C3×C72 | C2×D4 |
| LCS | G ▷ C2×C3×C72 ▷ C3×C72 | |
| UCS | C1 ◁ C22 | |
312 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72222125, C2×#72222096, C2×D3×#87641, … |
| maximal normal subgroup of | C2×#72222125, C2×#72222096, C2×D3×#87641, … |
| maximal quotient of | #72269409 |
Past the SmallGroups library coverage — no SmallGroups id.