Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C3 |
| direct product | C3⋊D3×#396 |
| Fitting | C32×#396 ⋊ C2 |
| Sylow | C32 ⋊ C2×#396 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×C3⋊D3 |
| commutator, socle, cosocle | C23×C32 | C24 |
| Fitting | C32×#396 | C2 |
| prime radical | C24×C3⋊D3 | C22 |
| hypercenter | #396 | C3⋊D3 |
| hypocenter | C32 | C2×#396 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ #396 | |
2724 conjugacy classes of subgroups; only the 359 normal subgroups are shown.
This group has 2724 conjugacy classes of subgroups — too many to draw. Only its 359 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 42265);