C₅×#5450 #11755461

order	960
isoclinism	isoclinic class of #5450
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅ · Schur multiplier (H₂) = C₂²

Aliases

	subgroup	G/H
center, hypercenter	C₅	#5450
commutator, cosocle, hypocenter	C₂⁴	C₂²×C₃×C₅
Frattini	C₂²	C₂²×C₅×A₄
Fitting	C₅×H(3,𝔽₄)	C₃
socle	C₂²×C₅	C₂²×A₄
LCS	G ▷ C₂⁴
UCS	C₁ ◁ C₅

140 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 2 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9656);