Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C32×C22⋊C4 ⋊ D4 |
| Sylow | C32 ⋊ #2361 |
1214 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^7,3^2|a^2=g,b^2=eg,d^2=e,b^a=be,c^a=cf,h^a=h^2i^2,i^a=h^2i,d^b=de,i^b=hi^2,h^d=hi,i^d=hi^2,h^e=h^2,i^e=i^2,h^g=h^2,i^g=i^290 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 40533);