Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | Dic3×#859 |
| derived | C3×SL(2,𝔽3) ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C23 | D3×S4 |
| commutator, hypocenter | C3×SL(2,𝔽3) | C42 |
| Fitting | C22×C3×Q8 | C2×D3 |
| socle | C23×C3 | C2×S4 |
| prime radical, cosocle | C22×C3×SL(2,𝔽3) | C22 |
| LCS | G ▷ C3×SL(2,𝔽3) | |
| UCS | C1 ◁ C23 | |
429 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 429 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 154677);