Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C7×SD16 ⋊ C2 |
| Sylow | C7 ⋊ #3120 |
372 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^b=h^6,f^c=fg116 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#3120, C2×#11737102, #14222155, … |
| maximal normal subgroup of | D7×#3120, C2×#11737102, #14222155, … |
| maximal quotient of | #13353902, #13356868, #13356908, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 11868);