Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×#10588301 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #63419 |
| commutator, cosocle, hypocenter | #95⋊C9 | C22 |
| Frattini | C23×C3 | C2×S4 |
| Fitting | C2×C3×#95 | D3 |
| socle, prime radical | C24×C3 | S4 |
| LCS | G ▷ #95⋊C9 | |
| UCS | C1 ◁ C22 | |
255 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 255 conjugacy classes of subgroups — too many to draw. Only its 29 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
54 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153949);