C₃×#124 #964

order	96
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	Aut(G) = C₂×#23900 (order 512) · Inn(G) = C₂³ · Out(G) = C₂³×D₄
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

	subgroup	G/H
center, socle	C₂²×C₃	C₂³
commutator, Frattini, cosocle	C₂²	C₂³×C₃
prime radical	C₂×C₃×D₄	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ G

76 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 48

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 171);