Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C32 ⋊ Q8×#41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D32 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C32×C4×Q8 | C22 |
| prime radical | C2×#3832 | C22 |
| hypercenter | C4×Q8 | D32 |
| hypocenter | C32 | Q8×#41 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
2291 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|a^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,d^b=df,h^b=h^2,i^b=i^2,i^c=hi^2,h^d=h^2,i^d=i^2,h^e=h^2,i^e=i^2120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 137807);