C₅×#6516 #11765111

order	1120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂⁴

Aliases

260 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 280

A minimal faithful permutation representation — 3 generators on 20 points:

(1,2,3,4,5)(6,7,9,11,12,10,8)(14,16);(18,20);(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)

310 conjugacy classes. The character table is too large to display.

maximal subgroup of	C₅×#10620789, D₅×#6516, C₅×D₇×#120, …
maximal normal subgroup of	C₅×#10620789, D₅×#6516, C₅×D₇×#120, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 717);