Finite Group DatabasebetaFinite Group Databasebeta| order | 2352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22×C7 |
| direct product | C22×C22⋊#3862 |
| Fitting, socle, Hall | C24×C72 ⋊ C3 |
| derived | C22×C72 ⋊ C22×C3 |
| Sylow | C72 ⋊ C22×A4 |
| Sylow | C24 ⋊ #3862 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | C22⋊#3862 |
| commutator, cosocle, hypocenter | C22×C72 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C24×C72 | C3 |
| LCS | G ▷ C22×C72 | |
| UCS | C1 ◁ C22 | |
290 conjugacy classes of subgroups.
272 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×#3861⋊A4, #72222229, #72222234, … |
| maximal normal subgroup of | C22×#3861⋊A4, #72222229, #72222234, … |
Past the SmallGroups library coverage — no SmallGroups id.