Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C4×C7×D4 ⋊ C2 |
| Sylow | C7 ⋊ #2325 |
696 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=g,c^2=f,b^a=be,c^a=cf,d^a=de,c^b=ce,h^c=h^6164 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2325, C2×#11739772, #13512601, … |
| maximal normal subgroup of | D7×#2325, C2×#11739772, #13512601, … |
| maximal quotient of | #13275050, #13275091, #13275098, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14538);