Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C22×#1007⋊C3 |
| Fitting | C23×C3×Q8 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D3×A4 |
| commutator, cosocle, hypocenter | C3×Q8 | C24×C3 |
| Frattini | C2 | C23×D3×A4 |
| Fitting | C23×C3×Q8 | C2×C3 |
| socle | C23×C3 | C22×A4 |
| hypercenter | C24 | D3×A4 |
| LCS | G ▷ C3×Q8 | |
| UCS | C1 ◁ C23 ◁ C24 | |
2657 conjugacy classes of subgroups; only the 271 normal subgroups are shown.
This group has 2657 conjugacy classes of subgroups — too many to draw. Only its 271 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157810);