Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C4×C7×D4 ⋊ C2 |
| Sylow | C7 ⋊ #2361 |
788 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=eg,d^2=e,b^a=be,c^a=cf,h^a=h^6,d^b=de,h^d=h^6170 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2361, C2×#11739785, #13513355, … |
| maximal normal subgroup of | D7×#2361, C2×#11739785, #13513355, … |
| maximal quotient of | C22⋊C4×Dic7⋊C4, #13275291, #13275294, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14551);