C₂×#3874 #64483

order	300
isoclinism	isoclinic class of #3874
automorphism	Aut(G) = C₂×#64480⋊C₂ (order 1200) · Inn(G) = #3874 · Out(G) = C₂×C₄
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

	subgroup	G/H
center, hypercenter	C₂	#3874
commutator, cosocle, hypocenter	C₅²⋊C₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₅²	D₃
LCS	G ▷ C₅²⋊C₃
UCS	C₁ ◁ C₂

30 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 30

A minimal faithful permutation representation — 2 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(300, 26);