Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×#3529⋊C3 |
| unambiguous semidirect product | #3529⋊C32 |
| unambiguous semidirect product | (C3×#3529)⋊C3 |
| Fitting | C3×#3529 ⋊ C3 |
| Sylow | #3529 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C4 | C22⋊A4 |
| commutator, cosocle, hypocenter | H(3,𝔽4) | C2×C32 |
| Frattini | C22 | C2×C3×C22⋊A4 |
| Fitting | C3×#3529 | C3 |
| socle | C22×C3 | C2×C22⋊A4 |
| LCS | G ▷ H(3,𝔽4) | |
| UCS | C1 ◁ C2×C3×C4 | |
550 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153851);