C₃×D₄×AΣL(1,𝔽₂₇) #14517819

order	1944
nilpotency class	3
isoclinism	isoclinic class of D₄×AΣL(1,𝔽₂₇)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃³ · Schur multiplier (H₂) = C₂×C₃³

Aliases

direct product	C₃×D₄×AΣL(1,𝔽₂₇)
unambiguous semidirect product	C₄⋊(C₂×C₃×AΣL(1,𝔽₂₇))

	subgroup	G/H
center, socle	C₂×C₃²	C₂²×H(3,𝔽₃)
commutator, Frattini, cosocle	C₂×C₃²	C₂²×C₃³
LCS	G ▷ C₂×C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₂×C₃² ◁ C₃³×D₄ ◁ G

1008 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 108

A minimal faithful permutation representation — 3 generators on 16 points:

(1,2,3)(13,14,15,16);(4,5,7)(6,8,11)(9,12,10)(14,16);(5,8,9)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 2213);