Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C32×C4⋊C4 ⋊ C22 |
| Sylow | C32 ⋊ #2342 |
1749 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^7,3^2|a^2=g,b^2=f,b^a=be,c^a=cf,i^a=hi^2,d^b=de,h^b=h^2,i^b=i^2,h^c=h^2,i^c=i^2,i^d=hi^2126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 39025);