Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of C22⋊(C22⋊A4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C29 |
| direct product | C2×C22⋊(C22⋊(C22⋊C9)) |
| derived | C26 ⋊ C2×C9 |
| Sylow | C27 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | C22⋊(C22⋊A4) |
| commutator, hypocenter | C26 | C2×C9 |
| Frattini | C3 | C2×C22⋊(C22⋊A4) |
| Fitting, socle, prime radical | C27×C3 | C3 |
| cosocle | C26×C3 | C2×C3 |
| LCS | G ▷ C26 | |
| UCS | C1 ◁ C2×C3 | |
19680 conjugacy classes of subgroups.
| transitive degree | μt(G) = 72 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153926);