C₂×C₃×C₅⋊D₅ #64502

order	300
isoclinism	isoclinic class of C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₂×C₃×C₅⋊D₅
unambiguous semidirect product	(C₂×C₅)⋊(C₃×D₅)

	subgroup	G/H
center, hypercenter	C₂×C₃	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₃

80 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 150

A minimal faithful permutation representation — 3 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(300, 45);