Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C7 ⋊ #3390 |
320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 896 |
Polycyclic presentation:
2^7,7|a^2=e,b^2=e,c^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^6,c^b=cg,d^b=de,f^c=fg104 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#3390, C2×#11741129, #14234353, … |
| maximal normal subgroup of | D7×#3390, C2×#11741129, #14234353, … |
| maximal quotient of | #13370476, #13370482, #13372119, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15895);