Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22×C7 |
| direct product | #41×#3862 |
| Fitting, Hall | C72×#41 ⋊ C3 |
| Sylow | C72 ⋊ C3×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×#3862 |
| commutator, socle, cosocle | C2×C72 | C23×C3 |
| Frattini | C2 | C23×#3862 |
| Fitting | C72×#41 | C3 |
| hypercenter | #41 | #3862 |
| hypocenter | C72 | C3×#41 |
| LCS | G ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C4 ◁ #41 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 168 |
190 conjugacy classes — view the full character table.
| maximal subgroup of | #41×#64425, AGL(1,ℤ/8)×#3862, #72245266, … |
| maximal normal subgroup of | #41×#64425, AGL(1,ℤ/8)×#3862, #72245266, … |
Past the SmallGroups library coverage — no SmallGroups id.