Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×#1790⋊C3 |
| unambiguous semidirect product | #1790⋊C32 |
| unambiguous semidirect product | (C3×#1790)⋊C3 |
| Fitting | C3×#1790 ⋊ C3 |
| derived | H(5,𝔽2) ⋊ C32×C4 |
| Sylow | #1790 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C22×C3 | #120⋊C3 |
| commutator, hypocenter | H(5,𝔽2) | C32×C4 |
| Frattini | C24 | C2×C3×A4 |
| Fitting | C3×#1790 | C3 |
| prime radical | C2×C3×#997 | C2 |
| cosocle | C2×H(5,𝔽2) | C2×C32 |
| LCS | G ▷ H(5,𝔽2) | |
| UCS | C1 ◁ C22×C3 | |
362 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 362 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) = 96 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153359);