C₃×#41×C₁₉ #11744995

order	912
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

C₃×#41×C₁₉

	subgroup	G/H
center	C₃×C₄×C₁₉	C₂²
commutator, Frattini, cosocle	C₂	C₂³×C₃×C₁₉
socle	C₂×C₃×C₁₉	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃×C₄×C₁₉ ◁ G

80 conjugacy classes of subgroups.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 456

A minimal faithful permutation representation — 3 generators on 30 points:

(1,2,3)(4,5)(6,9)(7,8)(10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30);(5,8)(9,11);(4,6,7,10)(5,9,8,11)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(912, 206);