Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of C22⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C27×C3 |
| direct product | C23×C3×C22⋊A4 |
| Fitting, socle | C27×C3 ⋊ C3 |
| derived | C24 ⋊ C23×C32 |
| Sylow | C27 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C3 | C22⋊A4 |
| commutator, cosocle, hypocenter | C24 | C23×C32 |
| Frattini | C1 | G |
| Fitting, socle | C27×C3 | C3 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C23×C3 | |
20072 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 20072 conjugacy classes of subgroups — too many to draw. Only its 288 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153927);