Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C16 · Schur multiplier (H2) = C8 |
| direct product | C3⋊C8×C3⋊C16 |
| derived, Sylow | C32 ⋊ C8×C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4×C8 | D32 |
| commutator, hypocenter | C32 | C8×C16 |
| Fitting, cosocle | C32×C4×C8 | C22 |
| socle, prime radical | C22×C32 | C4×C8 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C4×C8 | |
237 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 237 conjugacy classes of subgroups — too many to draw. Only its 140 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 5300);