C₅×C₂²⋊(C₄²⋊C₃) #11755472

order	960
isoclinism	isoclinic class of C₂²⋊(C₄²⋊C₃)
automorphism	?
homology	Abelianization (H₁) = C₃×C₅ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product	C₅×C₂²⋊(C₄²⋊C₃)
unambiguous semidirect product	C₂²⋊(C₅×C₄²⋊C₃)
unambiguous semidirect product	(C₂²×C₅)⋊(C₄²⋊C₃)

Fitting, Hall	C₂²×C₄²×C₅ ⋊ C₃
derived, Sylow	C₂²×C₄² ⋊ C₃×C₅

	subgroup	G/H
center, hypercenter	C₅	C₂²⋊(C₄²⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₄²	C₃×C₅
Frattini	C₂²	C₅×C₂²⋊A₄
Fitting	C₂²×C₄²×C₅	C₃
socle	C₂⁴×C₅	A₄
LCS	G ▷ C₂²×C₄²
UCS	C₁ ◁ C₅

206 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 120

A minimal faithful permutation representation — 3 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(960, 9667);