D₃²⋊#168 #13085573

order	1440
isoclinism	isoclinic class of D₃²⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂²

Aliases

	subgroup	G/H
center, Frattini, hypercenter	C₄	D₃²⋊D₅
commutator	C₅×C₃⋊D₃	C₂×C₈
Fitting	C₃²×C₄×C₅	D₄
socle	C₂×C₃²×C₅	C₂²⋊C₄
prime radical	C₂×C₅×D₃²	C₄
cosocle	C₄×C₅×C₃⋊D₃	C₂²
hypocenter	C₃²×C₅	C₂²⋊C₈
LCS	G ▷ C₅×C₃⋊D₃ ▷ C₃²×C₅
UCS	C₁ ◁ C₄

176 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.

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

μ_t(G) = 120

Polycyclic presentation:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 1890);