Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#72222113 |
| Hall | C3×C72 ⋊ C22×D4 |
| Sylow | C72 ⋊ C22×D12 |
| Sylow | C3 ⋊ C2×#11716115 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×D72 |
| commutator, cosocle | C2×C3×C72 | C24 |
| Frattini | C2 | C2×D3×D72 |
| Fitting, socle | C22×C3×C72 | C23 |
| hypocenter | C3×C72 | C22×D4 |
| LCS | G ▷ C2×C3×C72 ▷ C3×C72 | |
| UCS | C1 ◁ C22 | |
1346 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 1346 conjugacy classes of subgroups — too many to draw. Only its 172 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
252 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#11716115, C2×#72222115 |
| maximal normal subgroup of | C2×D3×#11716115, C2×#72222115 |
| maximal quotient of | #72269378 |
Past the SmallGroups library coverage — no SmallGroups id.