Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C32×C4⋊C4 ⋊ C22 |
| Sylow | C32 ⋊ C2×#539 |
2497 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|b^2=g,c^2=f,b^a=bf,c^a=cg,d^a=df,i^a=hi^2,c^b=cf,h^e=h^2,i^e=i^2108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 135408);