D₃×C₅⋊D₅ #64495

order	300
isoclinism	isoclinic class of D₃×C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	D₃×C₅⋊D₅
unambiguous semidirect product	(C₅×D₃)⋊D₅

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅²	C₂²
LCS	G ▷ C₃×C₅²
UCS	C₁

80 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 75

A minimal faithful permutation representation — 3 generators on 13 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(300, 38);