Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C7 ⋊ #3243 |
320 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|b^2=eg,c^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,f^c=fg,h^c=h^692 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#3243, C2×#11740899, #14226043, … |
| maximal normal subgroup of | D7×#3243, C2×#11740899, #14226043, … |
| maximal quotient of | #13363341, #13363567, #13364390, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 15665);