C₂²⋊C₄×SL(2,𝔽₅) #14514949

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂²

Aliases

direct product	C₂²⋊C₄×SL(2,𝔽₅)
unambiguous semidirect product	C₂²⋊(C₄×SL(2,𝔽₅))

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

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

normal subgroups only

This group has 484 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) = 192

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240647);