#14522936

order	2000
isoclinism	isoclinic class of #14522936
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₄

Aliases

No aliases for this group.

C₅³ ⋊ C₄²

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅³	C₄²
prime radical, cosocle	D₅×C₅⋊D₅	C₂²
LCS	G ▷ C₅³
UCS	C₁

172 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 29 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|a^2=c,b^2=d,e^a=e^4,g^a=g^2,e^b=e^2,f^b=f^2,g^c=g^4,e^d=e^4,f^d=f^4

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 899);