Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C3×C4 |
No aliases for this group.
| Fitting | C2×C32×C4⋊Q8 ⋊ C2 |
| Sylow | C32 ⋊ #2542 |
2028 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^7,3^2|a^2=ef,b^2=eg,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^2,i^a=i^2,c^b=cg,h^c=h^2,i^c=i^2150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 58496);