Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#73203 |
| Fitting | C3×#2811 ⋊ C3 |
| Sylow | #2811 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | #5450 |
| commutator, cosocle, hypocenter | C22×Q8 | C22×C32 |
| Frattini | C23 | C22×C3×A4 |
| Fitting | C3×#2811 | C3 |
| socle | C23×C3 | C22×A4 |
| prime radical | C3×C22⋊SL(2,𝔽3) | C22 |
| LCS | G ▷ C22×Q8 | |
| UCS | C1 ◁ C2×C3 | |
240 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153487);