Dic₅² #87777

order	400
isoclinism	isoclinic class of D₅²
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₄

Aliases

C₅² ⋊ C₄²

	subgroup	G/H
center, Frattini, hypercenter	C₂²	D₅²
commutator, hypocenter	C₅²	C₄²
Fitting, socle, prime radical, cosocle	C₂²×C₅²	C₂²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂²

76 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 80

A minimal faithful permutation representation — 2 generators on 18 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 71);