A₄⋊((C₂⁴⋊C₅)⋊C₂) #14514697

order	1920
isoclinism	isoclinic class of A₄⋊((C₂⁴⋊C₅)⋊C₂)
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₂³

Aliases

unambiguous semidirect product	A₄⋊((C₂⁴⋊C₅)⋊C₂)
unambiguous semidirect product	(C₂⁴⋊C₅)⋊S₄

Fitting, socle	C₂⁶ ⋊ D₁₅
derived	A₄×C₂⁴⋊C₅ ⋊ C₂

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	A₄×C₂⁴⋊C₅	C₂
Fitting, socle	C₂⁶	D₁₅
LCS	G ▷ A₄×C₂⁴⋊C₅
UCS	C₁

504 conjugacy classes of subgroups; only the 10 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 10 normal subgroups are shown.

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

μ_t(G) = 30

Polycyclic presentation:

2,3,5,2^6|b^a=b^2,c^a=c^4,d^a=de,f^a=fgi,h^a=hi,d^b=e,e^b=de,f^c=g,g^c=fgi,h^c=fh,i^c=fghi

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240395);