C₇⋊(Dic₁₁⋊C₅) #13095348

order	1540
isoclinism	isoclinic class of C₇⋊AGL(1,𝔽₁₁)
automorphism	?
homology	Abelianization (H₁) = C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₇⋊(Dic₁₁⋊C₅)
unambiguous semidirect product	(C₁₁⋊C₅)⋊Dic₇
unambiguous semidirect product	Dic₇₇⋊C₅

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₇⋊AGL(1,𝔽₁₁)
commutator, hypocenter	C₇×C₁₁	C₄×C₅
Fitting, socle, cosocle	C₂×C₇×C₁₁	C₂×C₅
prime radical	C₂×C₇×C₁₁⋊C₅	C₂
LCS	G ▷ C₇×C₁₁
UCS	C₁ ◁ C₂

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 308

Polycyclic presentation:

2,5,2,7,11|a^2=c,d^a=d^6,e^a=e^10,e^b=e^3

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1540, 3);