Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | C4×#63432 |
| Sylow | C9 ⋊ C4×#125 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D9 |
| commutator | C22×C9 | C23×C4 |
| Frattini, socle, prime radical | C23×C3 | C23×D3 |
| Fitting | C43×C9 | C2 |
| cosocle | C23×C9 | C24 |
| hypercenter | C43 | D9 |
| hypocenter | C9 | C4×#125 |
| LCS | G ▷ C22×C9 ▷ C9 | |
| UCS | C1 ◁ C22×C4 ◁ C43 | |
726 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1152 |
312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 36483);