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×M16 ⋊ C2 |
| Sylow | C7 ⋊ #2967 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D7 |
| commutator, socle | C22×C7 | C23×C4 |
| Fitting | C4×C7×M16 | C2 |
| prime radical | #6493 | C4 |
| cosocle | C2×C4×C7 | C24 |
| hypercenter | C4×M16 | D7 |
| hypocenter | C7 | #2967 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C2×C4 ◁ C4×M16 | |
362 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|a^2=f,c^2=f,d^2=e,f^2=g,b^a=be,d^a=dg,h^a=h^6,c^b=cg164 conjugacy classes — view the full character table.
| maximal subgroup of | #13251012, #13251016, #13251019, … |
| maximal normal subgroup of | #13251012, #13251016, #13251019, … |
| maximal quotient of | #13352035, #13352053, #13352152, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 10721);