Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #3556⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C24×C3 |
| direct product | C3×#3556⋊C3 |
| unambiguous semidirect product | #3556⋊C32 |
| unambiguous semidirect product | (C3×#3556)⋊C3 |
| Fitting | C3×#3556 ⋊ C3 |
| derived | #564 ⋊ C2×C32 |
| Sylow | #3556 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #3556⋊C3 |
| commutator, cosocle, hypocenter | #564 | C2×C32 |
| Frattini | C22 | C2×C3×C22⋊A4 |
| Fitting | C3×#3556 | C3 |
| socle | C22×C3 | C2×C22⋊A4 |
| LCS | G ▷ #564 | |
| UCS | C1 ◁ C3 | |
382 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
54 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153859);