Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D3×D96 |
| Fitting | C32×C32 ⋊ C22 |
| Sylow | C32 ⋊ C2×D32 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D3×D48 |
| commutator, cosocle | C32×C16 | C23 |
| Frattini | C16 | C2×D32 |
| Fitting | C32×C32 | C22 |
| socle | C2×C32 | C2×D16 |
| hypercenter | C32 | D32 |
| hypocenter | C32 | C2×D32 |
| LCS | G ▷ C32×C16 ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32 | |
257 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 257 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
153 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 34517);