Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C22×C7×C4⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ #2311 |
880 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=g,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^6,c^b=ce,h^c=h^6164 conjugacy classes — view the full character table.
| maximal subgroup of | #13259122, #13259190, #13260191, … |
| maximal normal subgroup of | #13259122, #13259190, #13260191, … |
| maximal quotient of | #13275044, #13275097, #13275100, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14397);