Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×#5931 |
| Fitting | C23×C3×Q8 ⋊ D3 |
| derived | C22⋊SL(2,𝔽3) ⋊ C22×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #1020 |
| commutator, cosocle, hypocenter | C22⋊SL(2,𝔽3) | C22×C3 |
| Frattini | C2 | C2×C3×#1020 |
| Fitting | C23×C3×Q8 | D3 |
| socle | C24×C3 | S4 |
| LCS | G ▷ C22⋊SL(2,𝔽3) | |
| UCS | C1 ◁ C22×C3 | |
640 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157759);