C₅×C₁₁⋊D₁₁ #11925906

order	1210
isoclinism	isoclinic class of C₁₁⋊D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₁₁

Aliases

C₅×C₁₁⋊D₁₁

Fitting, socle, Hall	C₅×C₁₁² ⋊ C₂
derived, Sylow	C₁₁² ⋊ C₂×C₅

	subgroup	G/H
center, hypercenter	C₅	C₁₁⋊D₁₁
commutator, cosocle, hypocenter	C₁₁²	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₁₁²	C₂
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₅

56 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 605

A minimal faithful permutation representation — 3 generators on 27 points:

(1,2,3,4,5)(7,8)(9,10)(11,12)(13,14)(15,16)(18,19)(20,21)(22,23)(24,25)(26,27);(17,18,20,22,24,26,27,25,23,21,19);(6,7,9,11,13,15,16,14,12,10,8)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1210, 23);