D₁₁² #92151

order	484
isoclinism	isoclinic class of D₁₁²
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	D₁₁²
unambiguous semidirect product	(C₁₁×D₁₁)⋊C₂
unambiguous semidirect product	(C₁₁⋊D₁₁)⋊C₂

C₁₁² ⋊ C₂²

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₁²	C₂²
LCS	G ▷ C₁₁²
UCS	C₁

30 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 22

A minimal faithful permutation representation — 2 generators on 22 points:

(1,5,7,13,15,21,20,18,12,10,4,2,3,9,11,17,19,22,16,14,8,6);(1,5,8,13,16,21,19,18,11,10,3,2,4,9,12,17,20,22,15,14,7,6)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(484, 9);