Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #2352 |
660 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=f,c^2=f,b^a=be,c^a=cf,h^a=h^6,d^b=de170 conjugacy classes — view the full character table.
| maximal subgroup of | #13369213, #13369215, #13369239, … |
| maximal normal subgroup of | #13369213, #13369215, #13369239, … |
| maximal quotient of | C22⋊C4×C4⋊Dic7, #13275219, #13275240, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 14546);