Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#66675 |
| Hall | C3×C72 ⋊ #41 |
| Sylow | C72 ⋊ #235 |
| Sylow | C3 ⋊ C7×#1157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C7 | D3×D7 |
| commutator, cosocle | C2×C3×C7 | C23×C7 |
| Frattini | C2 | C2×D3×C7×D7 |
| Fitting | C3×C4×C72 | C22 |
| socle | C2×C3×C72 | C23 |
| hypocenter | C3×C7 | C7×#41 |
| LCS | G ▷ C2×C3×C7 ▷ C3×C7 | |
| UCS | C1 ◁ C4×C7 | |
208 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
378 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C7×#1157, #72254280, #72254281, … |
| maximal normal subgroup of | D3×C7×#1157, #72254280, #72254281, … |
Past the SmallGroups library coverage — no SmallGroups id.