Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C8 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C3×#504⋊C3 |
| unambiguous semidirect product | (C2×#504)⋊C32 |
| unambiguous semidirect product | (C2×C3×#504)⋊C3 |
| Fitting | C2×C3×#504 ⋊ C3 |
| Sylow | C2×#504 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C16 | A4 |
| commutator, hypocenter | Q8 | C2×C32×C8 |
| Frattini | C8 | C22×C3×A4 |
| Fitting | C2×C3×#504 | C3 |
| socle | C22×C3 | C8×A4 |
| prime radical | C2×C3×#41⋊C3 | C4 |
| cosocle | #131 | C22×C32 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C2×C3×C16 | |
256 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
336 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153631);