Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #2069⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×#2069⋊C3 |
| unambiguous semidirect product | #2069⋊C32 |
| unambiguous semidirect product | (C3×#2069)⋊C3 |
| Fitting | C3×#2069 ⋊ C3 |
| derived | #338 ⋊ C2×C32 |
| Sylow | #2069 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | #396⋊C3 |
| commutator, cosocle, hypocenter | #338 | C2×C32 |
| Frattini | C22×C4 | C2×C3×A4 |
| Fitting | C3×#2069 | C3 |
| hypercenter | C3×C4 | #126⋊C3 |
| LCS | G ▷ #338 | |
| UCS | C1 ◁ C2×C3 ◁ C3×C4 | |
168 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
63 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153381);