Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #95⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#1726⋊C3 |
| unambiguous semidirect product | #1726⋊C32 |
| unambiguous semidirect product | (C3×#1726)⋊C3 |
| Fitting | C3×#1726 ⋊ C3 |
| Sylow | #1726 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C8 | C42⋊C3 |
| commutator, hypocenter | #95 | C32×C4 |
| Frattini | C22×C4 | C2×C3×A4 |
| Fitting | C3×#1726 | C3 |
| socle | C23×C3 | C4×A4 |
| prime radical | C3×#95⋊C3 | C4 |
| cosocle | #376 | C2×C32 |
| LCS | G ▷ #95 | |
| UCS | C1 ◁ C3×C8 | |
168 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153349);