#2657⋊C₃ #73197

order	384
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₄

Aliases

	subgroup	G/H
center	C₂	C₂×#127⋊C₃
commutator, cosocle, hypocenter	#95	C₂²×C₃
Frattini, socle	C₂³	C₂²×A₄
Fitting	#2657	C₃
hypercenter	C₄	#127⋊C₃
LCS	G ▷ #95
UCS	C₁ ◁ C₂ ◁ C₄

169 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 24

A minimal faithful permutation representation — 2 generators on 24 points:

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

Polycyclic presentation:

2^2,3,2^5|a^2=f,b^2=f,d^2=fg,e^2=fh,b^a=bf,c^a=cg,d^a=dg,e^a=eh,d^c=egh,e^c=defg,g^c=h,h^c=gh,e^d=ef

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 5773);