Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| direct product | C3×#73031 |
| Fitting | C3×#458 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C2×C3 | #1020⋊C2 |
| commutator, cosocle, hypocenter | #997 | C22×C3 |
| Frattini | C23 | C2×C3×S4 |
| Fitting | C3×#458 | D3 |
| prime radical | C3×#5935 | C2 |
| LCS | G ▷ #997 | |
| UCS | C1 ◁ C2×C3 | |
263 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 263 conjugacy classes of subgroups — too many to draw. Only its 22 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#11714182, #72274907, #72274915, … |
| maximal normal subgroup of | C3×#11714182, #72274907, #72274915, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154820);