Dic₃⋊#157 #88922

order	432
isoclinism	isoclinic class of (C₂×D₃)⋊#157
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂×C₃

Aliases

C₃³ ⋊ C₄⋊C₄

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×#157
commutator, Fitting, socle	C₂×C₃³	C₂×C₄
prime radical, cosocle	C₂×C₃×C₃⋊D₃	C₂²
hypocenter	C₃³	C₄⋊C₄
LCS	G ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂

96 conjugacy classes of subgroups.

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 13 points:

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

Polycyclic presentation:

2^4,3^3|a^2=d,b^2=c,b^a=bd,g^a=g^2,e^b=e^2f,f^b=ef,e^c=e^2,f^c=f^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 569);