Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×#10596874 |
| derived, Sylow | C72 ⋊ C22×C3×C4 |
| Hall | C22×C7⋊Dic7 ⋊ C3 |
| Hall | #3861 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #64424 |
| commutator, hypocenter | C72 | C22×C3×C4 |
| Frattini | C2 | C22×#64424 |
| Fitting, socle | C23×C72 | C2×C3 |
| prime radical | C23×#3861 | C2 |
| cosocle | C2×C72 | C23×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C23 | |
540 conjugacy classes of subgroups.
| transitive degree | μt(G) = 784 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | C22×C4×#64424, C22×#15668765, #72243538, … |
| maximal normal subgroup of | C22×C4×#64424, #72243538, C22×#11924217, … |
| maximal quotient of | C22×#15668765, C2×D3×#10596874, C2×#72228635, … |
Past the SmallGroups library coverage — no SmallGroups id.