Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×C7×C22⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ #2342 |
792 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=f,b^a=be,c^a=cf,d^b=de,h^c=h^6170 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2342, C2×#11731019, #13513065, … |
| maximal normal subgroup of | D7×#2342, C2×#11731019, #13513065, … |
| maximal quotient of | C22⋊C4×(C2×D7)⋊C4, #13275206, #13275230, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5785);