C₁₁×(C₂⁴⋊C₅)⋊C₂ #13183461

order	1760
isoclinism	isoclinic class of (C₂⁴⋊C₅)⋊C₂
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₁₁×(C₂⁴⋊C₅)⋊C₂
unambiguous semidirect product	(C₂⁴⋊C₅)⋊(C₂×C₁₁)

Fitting, socle	C₂⁴×C₁₁ ⋊ D₅
derived	C₂⁴⋊C₅ ⋊ C₂×C₁₁

	subgroup	G/H
center, hypercenter	C₁₁	(C₂⁴⋊C₅)⋊C₂
commutator, cosocle, hypocenter	C₂⁴⋊C₅	C₂×C₁₁
Frattini	C₁	G
Fitting, socle	C₂⁴×C₁₁	D₅
LCS	G ▷ C₂⁴⋊C₅
UCS	C₁ ◁ C₁₁

86 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 110

A minimal faithful permutation representation — 2 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 1270);