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×Q8 ⋊ C2 |
| Sylow | C7 ⋊ #2360 |
620 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=g,d^2=e,b^a=be,c^a=cf,d^b=de,h^c=h^6170 conjugacy classes — view the full character table.
| maximal subgroup of | #13374047, #13374056, #13374122, … |
| maximal normal subgroup of | #13374047, #13374056, #13374122, … |
| maximal quotient of | C4⋊C4×(C2×D7)⋊C4, #13275304, #13275334, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14701);