Finite Group DatabasebetaFinite Group Databasebeta| order | 4704 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#11924174 |
| derived, Sylow | C72 ⋊ C23×C3×C4 |
| Hall | C22×#87639 ⋊ C3 |
| Hall | #3861 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #64423⋊C2 |
| commutator, hypocenter | C72 | C23×C3×C4 |
| Frattini | C2 | C22×#64423⋊C2 |
| Fitting, socle | C23×C72 | C22×C3 |
| prime radical | C23×#64424 | C2 |
| cosocle | C2×C72 | C24×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C23 | |
1346 conjugacy classes of subgroups; only the 306 normal subgroups are shown.
This group has 1346 conjugacy classes of subgroups — too many to draw. Only its 306 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
152 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#72210376, C2×D3×#11924174, C2×#72214252 |
| maximal normal subgroup of | C22×#72210376, C2×#72214252 |
| maximal quotient of | C2×D3×#11924174 |
Past the SmallGroups library coverage — no SmallGroups id.