Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D3×#4676 |
| Fitting | C32×#95 ⋊ C22 |
| Sylow | C32 ⋊ C2×#396 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D32 |
| commutator, socle, cosocle | C23×C32 | C24 |
| Fitting | C32×#95 | C22 |
| prime radical | C23×D32 | C22 |
| hypercenter | #95 | D32 |
| hypocenter | C32 | C2×#396 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ #95 | |
1909 conjugacy classes of subgroups; only the 304 normal subgroups are shown.
This group has 1909 conjugacy classes of subgroups — too many to draw. Only its 304 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 42287);