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 ⋊ #2364 |
716 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=g,c^2=ef,b^a=be,c^a=cf,d^b=de,h^c=h^6170 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2364, C2×#11739787, #13513409, … |
| maximal normal subgroup of | D7×#2364, C2×#11739787, #13513409, … |
| maximal quotient of | #13275225, #13275291, #13275294, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14553);