C₅²×GL(2,𝔽₃) #11925462

order	1200
isoclinism	isoclinic class of #226
automorphism	?
homology	Abelianization (H₁) = C₂×C₅² · Schur multiplier (H₂) = C₅

Aliases

Fitting	C₅²×Q₈ ⋊ D₃
derived	SL(2,𝔽₃) ⋊ C₂×C₅²

	subgroup	G/H
center, socle, hypercenter	C₂×C₅²	S₄
commutator, cosocle, hypocenter	SL(2,𝔽₃)	C₂×C₅²
Frattini	C₂	C₅²×S₄
Fitting	C₅²×Q₈	D₃
LCS	G ▷ SL(2,𝔽₃)
UCS	C₁ ◁ C₂×C₅²

128 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 200

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 672);