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 ⋊ #2366 |
832 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=eg,c^2=f,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 | #13376035, #13376037, #13376057, … |
| maximal normal subgroup of | #13376035, #13376037, #13376057, … |
| maximal quotient of | C4⋊C4×Dic7⋊C4, #13275361, #13275363, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14554);