C₃³×#41 #89086

order	432
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃³ · Schur multiplier (H₂) = C₂²×C₃³

Aliases

C₃³×#41

	subgroup	G/H
center	C₃³×C₄	C₂²
commutator, Frattini, cosocle	C₂	C₂³×C₃³
socle	C₂×C₃³	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃³×C₄ ◁ G

560 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 216

A minimal faithful permutation representation — 3 generators on 17 points:

(1,2)(3,6)(4,5)(7,8)(9,10,11);(2,5)(6,8)(12,13,14);(1,3,4,7)(2,6,5,8)(15,16,17)

270 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 733);