Finite Group DatabasebetaFinite Group Databasebeta| order | 896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C7×Q82 ⋊ C2 |
| Sylow | C7 ⋊ #3483 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D7 |
| commutator, socle, cosocle | C22×C7 | C25 |
| Fitting | C7×Q82 | C2 |
| hypercenter | Q82 | D7 |
| hypocenter | C7 | #3483 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C22 ◁ Q82 | |
1202 conjugacy classes of subgroups; only the 491 normal subgroups are shown.
This group has 1202 conjugacy classes of subgroups — too many to draw. Only its 491 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 448 |
Polycyclic presentation:
2^7,7|b^2=f,c^2=f,d^2=f,e^2=fg,b^a=bf,c^a=cg,h^a=h^6,d^b=df,h^c=h^6,h^e=h^6125 conjugacy classes — view the full character table.
| maximal subgroup of | #13329690, #13329696, #13329734, … |
| maximal normal subgroup of | #13329690, #13329696, #13329734, … |
| maximal quotient of | #13513276, #13513576, #13513648, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(896, 18874);