Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C7 ⋊ #3367 |
372 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|b^2=eg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,f^c=fg,h^d=h^686 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#3367, C2×#11737963, #14233602, … |
| maximal normal subgroup of | D7×#3367, C2×#11737963, #14233602, … |
| maximal quotient of | #13370427, #13370624, #13372776, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 12729);