#2675⋊C₃ #73199

order	384
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂²

Aliases

	subgroup	G/H
center, hypercenter	C₂	#560⋊C₃
commutator, cosocle, hypocenter	#95	C₂²×C₃
Frattini, socle	C₂³	C₂²×A₄
Fitting	#2675	C₃
LCS	G ▷ #95
UCS	C₁ ◁ C₂

169 conjugacy classes of subgroups.

minimal degree	μ(G) = 12
transitive degree	μ_t(G) = 12

A minimal faithful permutation representation — 2 generators on 12 points:

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

Polycyclic presentation:

2^2,3,2^5|a^2=fgh,d^2=g,e^2=h,b^a=bfgh,d^a=dfh,e^a=efg,c^b=cgh,d^b=dfg,e^b=egh,d^c=degh,e^c=d,f^c=h,g^c=f,h^c=g,e^d=efgh

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 5775);