Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×C7×C4⋊C4 ⋊ C2 |
| Hall | C5×C7 ⋊ #126 |
| Sylow | C7 ⋊ #4044 |
| Sylow | C5 ⋊ #6461 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D35 |
| commutator, socle, cosocle | C22×C5×C7 | C23 |
| Fitting | C5×C7×C4⋊C4 | C2 |
| prime radical | C22×D35 | C22 |
| hypercenter | C4⋊C4 | D35 |
| hypocenter | C5×C7 | #126 |
| LCS | G ▷ C22×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
120 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 560 |
Polycyclic presentation:
2^5,5,7|b^2=d,c^2=e,b^a=be,c^a=cd,f^a=f^4,g^a=g^6,c^b=ce184 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 834);