Dic₁₁₀ #89181

order	440
isoclinism	isoclinic class of Dic₁₁₀
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₁

Aliases

Dic₁₁₀

	subgroup	G/H
center, Frattini	C₂	C₂×D₅₅
commutator, socle, prime radical, cosocle	C₂×C₅×C₁₁	C₂²
Fitting	C₄×C₅×C₁₁	C₂
hypercenter	C₄	D₅₅
hypocenter	C₅×C₁₁	Q₈
LCS	G ▷ C₂×C₅×C₁₁ ▷ C₅×C₁₁
UCS	C₁ ◁ C₂ ◁ C₄

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 440

A minimal faithful permutation representation — 2 generators on 24 points:

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

Polycyclic presentation:

2^3,5,11|a^2=c,b^2=c,b^a=bc,d^a=d^4,e^a=e^10

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(440, 34);