C₄⋊C₄×SL(2,𝔽₅) #14514970

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₄⋊C₄×SL(2,𝔽₅)
unambiguous semidirect product	C₄⋊(C₄×SL(2,𝔽₅))

	subgroup	G/H
center, Frattini, socle, cosocle	C₂³	C₂²×A₅
commutator	C₂×SL(2,𝔽₅)	C₂×C₄
Fitting, hypercenter	C₂×C₄⋊C₄	A₅
prime radical	C₂²×SL(2,𝔽₅)	C₂²
hypocenter	SL(2,𝔽₅)	C₄⋊C₄
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

354 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.

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

μ_t(G) = 384

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240668);