Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×#64196 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D3×S4 |
| commutator, cosocle, hypocenter | C3×SL(2,𝔽3) | C24 |
| Frattini | C2 | C22×D3×S4 |
| Fitting | C22×C3×Q8 | C2×D3 |
| socle | C23×C3 | C2×S4 |
| prime radical | C22×C3⋊(#41⋊C3) | C2 |
| LCS | G ▷ C3×SL(2,𝔽3) | |
| UCS | C1 ◁ C23 | |
1529 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1529 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157566);