C₅×#66472 #13108535

order	1620
isoclinism	isoclinic class of #66472
automorphism	?
homology	Abelianization (H₁) = C₄×C₅ · Schur multiplier (H₂) = C₃⁴

Aliases

Fitting, socle, Hall	C₃⁴×C₅ ⋊ C₄
derived, Sylow	C₃⁴ ⋊ C₄×C₅

472 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 90

A minimal faithful permutation representation — 3 generators on 17 points:

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

maximal subgroup of	D₅×#66472, C₅×#10620198, #72269601, …
maximal normal subgroup of	D₅×#66472, C₅×#10620198, #72269601, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1620, 441);