Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Hall | C5×C7 ⋊ #120 |
| Sylow | C7 ⋊ #4099 |
| Sylow | C5 ⋊ #6445 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D5×D7 |
| commutator, socle, cosocle | C22×C5×C7 | C23 |
| Fitting | C23×C5×C7 | C22 |
| hypercenter | C23 | D5×D7 |
| hypocenter | C5×C7 | #120 |
| LCS | G ▷ C22×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C22 ◁ C23 | |
260 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 280 |
Polycyclic presentation:
2^5,5,7|b^2=e,b^a=be,g^a=g^6,c^b=cd,f^b=f^4124 conjugacy classes — view the full character table.
| maximal subgroup of | #72218371, D5×#6445, D7×#4099, … |
| maximal normal subgroup of | #72218371, D5×#6445, D7×#4099, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 614);