Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C9 · Schur multiplier (H2) = C211 |
| direct product | C25×C22⋊C9 |
| derived | C22 ⋊ C25×C9 |
| Sylow | C27 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25×C3 | A4 |
| commutator, hypocenter | C22 | C25×C9 |
| Frattini | C3 | C25×A4 |
| Fitting, socle, prime radical | C27×C3 | C3 |
| cosocle | C22×C3 | C25×C3 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C25×C3 | |
21220 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
384 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153930);