C₅×D₃²×D₅ #14268482

order	1800
isoclinism	isoclinic class of D₃²×D₅
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅ · Schur multiplier (H₂) = C₂³

Aliases

direct product	C₅×D₃²×D₅
unambiguous semidirect product	(C₃×D₃×D₅)⋊(C₂×C₅)
unambiguous semidirect product	(D₅×C₃⋊D₃)⋊(C₂×C₅)
unambiguous semidirect product	(D₃×D₁₅)⋊(C₂×C₅)

	subgroup	G/H
center, hypercenter	C₅	D₃²×D₅
commutator, cosocle, hypocenter	C₃²×C₅	C₂³×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅²	C₂³
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₅

320 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.

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

μ_t(G) = 60

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1800, 676);