Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C7×H(5,𝔽2) ⋊ C2 |
| Sylow | C7 ⋊ #3500 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D7 |
| commutator, socle, cosocle | C22×C7 | C25 |
| Fitting | C2×C7×H(5,𝔽2) | C2 |
| hypercenter | C2×H(5,𝔽2) | D7 |
| hypocenter | C7 | #3500 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ C2×H(5,𝔽2) | |
1540 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^7,7|c^2=fg,e^2=f,b^a=bf,c^a=cg,e^a=ef,d^b=df,h^c=h^6146 conjugacy classes — view the full character table.
| maximal subgroup of | #13269366, #13362998, #13363005, … |
| maximal normal subgroup of | #13269366, #13362998, #13363005, … |
| maximal quotient of | #13513903, #13514178, #13514211, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 19117);