(D₅⋊AGL(1,𝔽₅))⋊D₅ #14522959

order	2000
isoclinism	isoclinic class of (D₅⋊AGL(1,𝔽₅))⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

C₅³ ⋊ #41

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle	C₅×C₅⋊D₅	C₂³
Fitting, socle, hypocenter	C₅³	#41
LCS	G ▷ C₅×C₅⋊D₅ ▷ C₅³
UCS	C₁

140 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

μ_t(G) = 40

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 922);