Finite Group DatabasebetaFinite Group Databasebeta| order | 1120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C5×C7 ⋊ D16 |
| Sylow | C7 ⋊ D80 |
| Sylow | C5 ⋊ #6400 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #10587843 |
| commutator, Fitting, cosocle | C5×C7×C8 | C22 |
| Frattini, hypercenter | C8 | D5×D7 |
| socle | C2×C5×C7 | D8 |
| hypocenter | C5×C7 | D16 |
| LCS | G ▷ C5×C7×C8 ▷ C4×C5×C7 ▷ C2×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 560 |
Polycyclic presentation:
2^5,5,7|a^2=c,c^2=de,d^2=e,b^a=bc,g^a=g^6,c^b=cd,d^b=de,f^b=f^4112 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1120, 15);