Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C7×#532 ⋊ C2 |
| Sylow | C7 ⋊ D4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D7 |
| commutator, socle, cosocle | C22×C7 | C25 |
| Frattini | C22 | C24×D7 |
| Fitting | C7×#532 | C2 |
| hypercenter | #532 | D7 |
| hypocenter | C7 | D4×#41 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C2×C4 ◁ #532 | |
1648 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|e^2=f,b^a=bf,c^a=cg,h^a=h^6,d^b=df,h^b=h^6,h^c=h^6134 conjugacy classes — view the full character table.
| maximal subgroup of | #13245815, #13245819, #13320654, … |
| maximal normal subgroup of | #13245815, #13245819, #13320654, … |
| maximal quotient of | #13512997, #13513107, #13513197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 18072);