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 ⋊ #2321 |
808 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=g,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 | #13249330, #13249340, #13359801, … |
| maximal normal subgroup of | #13249330, #13249340, #13359801, … |
| maximal quotient of | #13275034, #13275081, #13275091, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5780);