Dic₅×S₄ #91900

order	480
isoclinism	isoclinic class of D₅×S₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂²

Aliases

derived	C₅×A₄ ⋊ C₂×C₄
Sylow	C₅ ⋊ C₄×S₄

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅×S₄
commutator, hypocenter	C₅×A₄	C₂×C₄
Fitting, socle	C₂³×C₅	C₂×D₃
prime radical	C₂×C₅×S₄	C₂
cosocle	C₂×C₅×A₄	C₂²
LCS	G ▷ C₅×A₄
UCS	C₁ ◁ C₂

112 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 60

A minimal faithful permutation representation — 2 generators on 13 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 976);