Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C25 |
| direct product | #67×C22⋊A4 |
| Fitting | C26×C3 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D3×C22⋊A4 |
| commutator, socle, cosocle | C25×C3 | C22×C3 |
| Fitting | C26×C3 | C2×C3 |
| hypercenter | C22 | D3×C22⋊A4 |
| hypocenter | C24×C3 | C3×D4 |
| LCS | G ▷ C25×C3 ▷ C24×C3 | |
| UCS | C1 ◁ C2 ◁ C22 | |
3739 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 3739 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157848);