C₂²×#95⋊C₃ #73159

order	384
isoclinism	isoclinic class of #95⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂²

Aliases

Fitting, Sylow	C₂²×#95 ⋊ C₃
derived	#95 ⋊ C₂²×C₃

	subgroup	G/H
center, hypercenter	C₂³	C₄²⋊C₃
commutator, cosocle, hypocenter	#95	C₂²×C₃
Frattini	C₂³	C₂²×A₄
Fitting	C₂²×#95	C₃
socle	C₂⁵	A₄
LCS	G ▷ #95
UCS	C₁ ◁ C₂³

375 conjugacy classes of subgroups.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 16 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 5735);