Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| isoclinism | isoclinic class of #2865⋊C7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #2865⋊C7 |
| Fitting, Sylow | #2865 ⋊ C7 |
| derived | C43 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C43 | C2×C7 |
| Frattini, socle | C23 | C2×AGL(1,𝔽8) |
| Fitting | #2865 | C7 |
| LCS | G ▷ C43 | |
| UCS | C1 | |
41 conjugacy classes of subgroups.
| minimal degree | μ(G) = 56 |
| transitive degree | μt(G) = 56 |
Polycyclic presentation:
2,7,2^6|c^2=g,d^2=fgh,e^2=f,c^a=cf,d^a=dgh,e^a=eh,c^b=cdefg,d^b=cfh,e^b=ce,f^b=fg,g^b=h,h^b=fh20 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#2865⋊C7, #53385⋊C7, #53386⋊C7, … |
| maximal normal subgroup of | C2×#2865⋊C7, #53385⋊C7, #53386⋊C7, … |
| maximal quotient of | #14690⋊C7, C2×#2865⋊C7 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 5503);