Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C5×C7 ⋊ #131 |
| Sylow | C7 ⋊ #4047 |
| Sylow | C5 ⋊ #6464 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D5×D7 |
| commutator, socle | C2×C5×C7 | C22×C4 |
| Frattini | C4 | C2×D5×D7 |
| Fitting | C5×C7×C8 | C22 |
| prime radical | #10587944 | C2 |
| cosocle | C4×C5×C7 | C23 |
| hypocenter | C5×C7 | #131 |
| LCS | G ▷ C2×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C8 | |
124 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 560 |
Polycyclic presentation:
2^5,5,7|c^2=d,d^2=e,b^a=be,g^a=g^6,f^b=f^4148 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 319);