Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C8×Q8⋊C9 |
| unambiguous semidirect product | (C2×C8×Q8)⋊C9 |
| derived | Q8 ⋊ C2×C8×C9 |
| Sylow | C2×C8×Q8 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3×C8 | A4 |
| commutator, hypocenter | Q8 | C2×C8×C9 |
| Frattini | C2×C3×C4 | C22×A4 |
| Fitting | C2×C3×C8×Q8 | C3 |
| socle, prime radical | C23×C3 | C4×A4 |
| cosocle | C3×C4×Q8 | C22×C3 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C22×C3×C8 | |
261 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 261 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1152 |
336 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153580);