C₂₇⋊AGL(1,𝔽₅) #10587346

order	540
isoclinism	isoclinic class of C₂₇⋊AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅×C₂₇	C₄
Frattini	C₉	ΓL(1,𝔽₁₆)
socle	C₃×C₅	Dic₉
prime radical	C₃×D₅	D₉
cosocle	D₅×C₂₇	C₂
LCS	G ▷ C₅×C₂₇
UCS	C₁

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 135

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(540, 6);