C₅×#64188 #13088259

order	1440
isoclinism	isoclinic class of #64188
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₂³

Aliases

	subgroup	G/H
center, hypercenter	C₅	#64188
commutator, cosocle, hypocenter	C₂²⋊(C₂²⋊C₉)	C₂×C₅
Frattini	C₃	C₅×#1020
Fitting, socle	C₂⁴×C₃×C₅	D₃
LCS	G ▷ C₂²⋊(C₂²⋊C₉)
UCS	C₁ ◁ C₅

202 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 180

A minimal faithful permutation representation — 2 generators on 22 points:

(1,2,3,4,5)(7,9)(8,12)(10,11)(13,14)(15,16,18,17)(19,20,22,21);(6,14,9,12,11,10,8,7,13)(16,17,18)(20,22,21)

maximal subgroup of	C₅×#11724027, C₅×#11724050, D₅×#64188
maximal normal subgroup of	C₅×#11724050, D₅×#64188

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4576);