C₄⋊(C₃⋊#157) #88991

order	432
isoclinism	isoclinic class of #88989
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂×C₃

Aliases

Fitting	C₃³×C₄ ⋊ C₄
Sylow	C₃³ ⋊ C₄⋊C₄

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:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 638);