Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C9 · Schur multiplier (H2) = C4 |
| direct product | C42×Q8⋊C9 |
| derived | Q8 ⋊ C42×C9 |
| Sylow | C42×Q8 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C42 | A4 |
| commutator, hypocenter | Q8 | C42×C9 |
| Frattini, socle, prime radical | C23×C3 | C22×A4 |
| Fitting | C3×C42×Q8 | C3 |
| cosocle | C22×C3×Q8 | C22×C3 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C2×C3×C42 | |
389 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 389 conjugacy classes of subgroups — too many to draw. Only its 153 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, 153410);