Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C7×#461 ⋊ C2 |
| Sylow | C7 ⋊ #3123 |
394 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^b=h^6,f^c=fg,h^d=h^689 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#3123, C2×#11737858, #14222164, … |
| maximal normal subgroup of | D7×#3123, C2×#11737858, #14222164, … |
| maximal quotient of | #13353889, #13356873, #13356875, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 12624);