C₃⋊(C₁₁⋊C₈) #63135

order	264
isoclinism	isoclinic class of D₃₃
automorphism	?
homology	Abelianization (H₁) = C₈ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₃⋊(C₁₁⋊C₈)
unambiguous semidirect product	C₁₁⋊(C₃⋊C₈)

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₃₃
commutator, hypocenter	C₃×C₁₁	C₈
Fitting, cosocle	C₃×C₄×C₁₁	C₂
socle, prime radical	C₂×C₃×C₁₁	C₄
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₄

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 264

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

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

Polycyclic presentation:

2^3,3,11|a^2=b,b^2=c,d^a=d^2,e^a=e^10

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(264, 3);