Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Sylow | C32 ⋊ C22⋊#95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C2×D32 |
| commutator | C22×C32 | C2×C42 |
| Fitting, prime radical | C25×C32 | C22 |
| socle, cosocle | C24×C32 | C23 |
| hypercenter | C25 | D32 |
| hypocenter | C32 | C22⋊#95 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C24 ◁ C25 | |
2857 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|a^2=f,b^2=g,b^a=bd,c^a=ce,i^a=hi^2,h^b=h^2,i^b=i^2168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 7177);