Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C7×#451 ⋊ C2 |
| Sylow | C7 ⋊ #3223 |
364 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=e,c^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,h^b=h^6,f^c=fg83 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#3223, C2×#11737625, #14225204, … |
| maximal normal subgroup of | D7×#3223, C2×#11737625, #14225204, … |
| maximal quotient of | #13363177, #13363586, #13364389, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 12391);