C₂²×C₅²⋊C₃ #64498

order	300
isoclinism	isoclinic class of C₅²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂×C₅

Aliases

C₂²×C₅²⋊C₃

Fitting, socle, Hall	C₂²×C₅² ⋊ C₃
derived, Sylow	C₅² ⋊ C₂²×C₃

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

30 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 60

A minimal faithful permutation representation — 2 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(300, 41);