D₄²×C₃₁ #14520726

order	1984
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃₁ · Schur multiplier (H₂) = C₂⁶

Aliases

D₄²×C₃₁

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₃₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ G

428 conjugacy classes of subgroups.

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 496

A minimal faithful permutation representation — 4 generators on 39 points:

(1,2,3,4)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39);(2,4);(5,6,7,8);(6,8)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1984, 226);