Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2×C7 |
| direct product | C8×#64425 |
| Fitting | C72×C8 ⋊ C2×C3 |
| derived, Sylow | C72 ⋊ C2×C3×C8 |
| Hall | C8×C7⋊D7 ⋊ C3 |
| Hall | #3862 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #64425 |
| commutator, hypocenter | C72 | C2×C3×C8 |
| Frattini | C4 | C2×#64425 |
| Fitting | C72×C8 | C2×C3 |
| socle | C2×C72 | C2×C3×C4 |
| prime radical | C2×#64425 | C4 |
| cosocle | C4×C72 | C22×C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C8 | |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | M16×#64425, SD16×#64425, D8×#64425, … |
| maximal normal subgroup of | M16×#64425, SD16×#64425, D8×#64425, … |
Past the SmallGroups library coverage — no SmallGroups id.