C₇⋊(Dic₃₁⋊C₅) #16864686

order	4340
automorphism	?
homology	Abelianization (H₁) = C₄×C₅ · Schur multiplier (H₂) = C₁

Aliases

unambiguous semidirect product	C₇⋊(Dic₃₁⋊C₅)
unambiguous semidirect product	ΓL(1,𝔽₃₂)⋊Dic₇
unambiguous semidirect product	Dic₂₁₇⋊C₅

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₇⋊(D₃₁⋊C₅)
commutator, hypocenter	C₇×C₃₁	C₄×C₅
Fitting, socle, cosocle	C₂×C₇×C₃₁	C₂×C₅
prime radical	C₂×C₇×ΓL(1,𝔽₃₂)	C₂
LCS	G ▷ C₇×C₃₁
UCS	C₁ ◁ C₂

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 42
transitive degree	μ_t(G) = 868

Polycyclic presentation:

2,5,7,31,2|a^2=e,c^a=c^6,d^a=d^30,d^b=d^16

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4340, 12);