C₅×#63419 #13083937

order	1440
isoclinism	isoclinic class of #63419
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, hypercenter	C₅	#63419
commutator, cosocle, hypocenter	C₄²⋊C₉	C₂×C₅
Frattini	C₂²×C₃	C₅×S₄
Fitting	C₃×C₄²×C₅	D₃
socle	C₂²×C₃×C₅	S₄
LCS	G ▷ C₄²⋊C₉
UCS	C₁ ◁ C₅

84 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 180

A minimal faithful permutation representation — 2 generators on 26 points:

(1,2,3,4,5)(6,8,9,13)(7,17,16,15,11,14,12,10)(19,21)(20,24)(22,23)(25,26);(6,7,10)(8,12,14)(9,11,15)(13,16,17)(18,26,21,24,23,22,20,19,25)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 254);