C₁₁⋊#170 #89163

order	440
isoclinism	isoclinic class of C₁₁⋊AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₈ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₁₁⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅×C₁₁	C₈
Fitting, socle, prime radical	C₂×C₅×C₁₁	C₄
cosocle	C₁₁×Dic₅	C₂
LCS	G ▷ C₅×C₁₁
UCS	C₁ ◁ C₂

16 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:

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

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(440, 16);