C₃⋊#3708 #88766

order	432
isoclinism	isoclinic class of C₃⋊#157
automorphism	?
homology	Abelianization (H₁) = C₁₆ · Schur multiplier (H₂) = C₃

Aliases

C₃³ ⋊ C₁₆

	subgroup	G/H
center, Frattini, hypercenter	C₄	C₃⋊#157
commutator, hypocenter	C₃³	C₁₆
Fitting	C₃³×C₄	C₄
socle, prime radical	C₂×C₃³	C₈
cosocle	C₃×C₃⋊(C₃⋊C₈)	C₂
LCS	G ▷ C₃³
UCS	C₁ ◁ C₄

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 25 points:

(1,2,3,6,4,7,9,12,5,8,10,13,11,14,15,16)(18,19)(20,21)(22,23,25,24);(17,18,19)(20,22,25)

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 413);