Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C7×#102 ⋊ C2 |
| Sylow | C7 ⋊ #3314 |
410 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|a^2=e,f^2=g,b^a=beg,c^a=cf,f^a=fg,c^b=cg,d^b=deg,h^b=h^6,f^c=fg113 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#3314, C2×#11736208, #14230561, … |
| maximal normal subgroup of | D7×#3314, C2×#11736208, #14230561, … |
| maximal quotient of | #13369272, #13370170, #13370893, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 10974);