Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C4 |
| direct product | C4×#10596874 |
| derived, Sylow | C72 ⋊ C3×C42 |
| Hall | C4×C7⋊Dic7 ⋊ C3 |
| Hall | #3861 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #64424 |
| commutator, hypocenter | C72 | C3×C42 |
| Frattini | C22 | C2×#64424 |
| Fitting | C2×C4×C72 | C2×C3 |
| socle, cosocle | C22×C72 | C22×C3 |
| prime radical | C22×#3861 | C22 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C4 | |
300 conjugacy classes of subgroups.
112 conjugacy classes — view the full character table.
| maximal subgroup of | C42×#64424, #72214755, #72214778, … |
| maximal normal subgroup of | C42×#64424, #72214755, #72214778, … |
| maximal quotient of | #72228589, #72228642 |
Past the SmallGroups library coverage — no SmallGroups id.