Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C7×#121 ⋊ C2 |
| Sylow | C7 ⋊ #3519 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D7 |
| commutator, socle, cosocle | C22×C7 | C25 |
| Fitting | C2×C7×#121 | C2 |
| hypercenter | C2×#121 | D7 |
| hypocenter | C7 | #3519 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C2×#121 | |
1252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|e^2=fg,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^b=h^6128 conjugacy classes — view the full character table.
| maximal subgroup of | #13320988, #13320994, #13321314, … |
| maximal normal subgroup of | #13320988, #13320994, #13321314, … |
| maximal quotient of | #13514007, #13514510, #13514511, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 17785);