Finite Group DatabasebetaFinite Group Databasebeta| order | 280 |
| isoclinism | isoclinic class of #63305 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C5×C7 ⋊ Q8 |
| Sylow | C7 ⋊ Dic10 |
| Sylow | C5 ⋊ Dic14 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×D7 |
| commutator, Fitting, socle, prime radical, cosocle | C2×C5×C7 | C22 |
| hypocenter | C5×C7 | Q8 |
| LCS | G ▷ C2×C5×C7 ▷ C5×C7 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 280 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,4,6,7,5,3)(9,10)(11,12)(13,15,16,20)(14,17,18,19);(2,3)(4,5)(6,7)(8,9,11,12,10)(13,14,16,18)(15,19,20,17)Polycyclic presentation:
2^3,5,7|a^2=c,b^2=c,b^a=bc,e^a=e^6,d^b=d^437 conjugacy classes — view the full character table.
| maximal subgroup of | D7×Dic10, D5×Dic14, D35⋊Q8, … |
| maximal normal subgroup of | D7×Dic10, D5×Dic14, D35⋊Q8, … |
| maximal quotient of | Dic7⋊Dic5, #10587858, #10587859, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(280, 13);