Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C7 |
| direct product | D8×#3862 |
| Fitting, Hall | C72×D8 ⋊ C3 |
| Sylow | C72 ⋊ C3×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×#3862 |
| commutator, cosocle | C4×C72 | C22×C3 |
| Frattini | C4 | C22×#3862 |
| Fitting | C72×D8 | C3 |
| socle | C2×C72 | C3×D4 |
| hypercenter | D8 | #3862 |
| hypocenter | C72 | C3×D8 |
| LCS | G ▷ C4×C72 ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D8 | |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
133 conjugacy classes — view the full character table.
| maximal subgroup of | D8×#64425, AGL(1,ℤ/8)×#3862, #72245257, … |
| maximal normal subgroup of | D8×#64425, AGL(1,ℤ/8)×#3862, #72245257, … |
Past the SmallGroups library coverage — no SmallGroups id.