Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of C22⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8 · Schur multiplier (H2) = C24×C3 |
| direct product | C3×C8×C22⋊A4 |
| Fitting | C24×C3×C8 ⋊ C3 |
| derived | C24 ⋊ C32×C8 |
| Sylow | C24×C8 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C8 | C22⋊A4 |
| commutator, hypocenter | C24 | C32×C8 |
| Frattini | C4 | C2×C3×C22⋊A4 |
| Fitting | C24×C3×C8 | C3 |
| socle | C25×C3 | C3×C4 |
| prime radical | C2×C3×C22⋊A4 | C4 |
| cosocle | C24×C4 | C2×C32 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C3×C8 | |
808 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 808 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) = 144 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153865);