#11757429⋊C₂ #14516523

order	1944
isoclinism	isoclinic class of #11757429⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₂²×C₂₇ ⋊ C₂×C₉

90 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 108

Polycyclic presentation:

2,3^2,2^2,3^3|b^3=c,f^3=g,g^3=h,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2,d^b=de,e^b=d,f^b=fg^2h,g^b=gh^2,f^c=fh^2

maximal subgroup of	A₄×AGL(1,ℤ/27)
maximal normal subgroup of	A₄×AGL(1,ℤ/27)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 917);