Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C32×C16 ⋊ C22 |
| Sylow | C32 ⋊ #3407 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×D32 |
| commutator, socle | C2×C32 | C23×C8 |
| Fitting | C2×C32×C16 | C22 |
| prime radical | #64306 | C4 |
| cosocle | C32×C8 | C24 |
| hypercenter | C2×C16 | D32 |
| hypocenter | C32 | #3407 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C8 ◁ C2×C16 | |
765 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|a^2=e,e^2=f,f^2=g,d^a=dg,c^b=cg,i^c=hi^2,h^d=h^2,i^d=i^2180 conjugacy classes — view the full character table.
| maximal subgroup of | #72222733 |
| maximal normal subgroup of | #72222733 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 133428);