Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C7×#451 ⋊ C2 |
| Sylow | C7 ⋊ D4×Q16 |
472 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=g,b^2=g,d^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,h^a=h^6,d^b=de,e^b=eg,h^b=h^6,e^d=eg92 conjugacy classes — view the full character table.
| maximal subgroup of | D4×D7×Q16, C2×#11737656, #14229084, … |
| maximal normal subgroup of | D4×D7×Q16, C2×#11737656, #14229084, … |
| maximal quotient of | #13343976, #13343981, #13343986, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 12422);