Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C32×#107 ⋊ C22 |
| Sylow | C32 ⋊ C2×C4×D8 |
1297 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|a^2=f,c^2=f,e^2=g,b^a=be,e^a=eg,e^b=eg,i^b=hi^2,i^c=hi^2,h^d=h^2,i^d=i^2126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 93858);