Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | D3×#5231 |
| Fitting | C22×C32×Q8 ⋊ C22 |
| Sylow | C32 ⋊ C2×#393 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D32 |
| commutator, socle, cosocle | C23×C32 | C24 |
| Fitting | C22×C32×Q8 | C22 |
| prime radical | C23×D32 | C22 |
| hypercenter | C22×Q8 | D32 |
| hypocenter | C32 | C2×#393 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
2173 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 42127);