Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C7×C4⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ #2373 |
496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=g,c^2=e,d^2=ef,b^a=be,c^a=cf,d^b=de,h^b=h^6170 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#2373, C2×#11731109, #13513498, … |
| maximal normal subgroup of | D7×#2373, C2×#11731109, #13513498, … |
| maximal quotient of | #13275253, #13275316, #13275327, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5875);