#170×GL(2,𝔽₃) #14512394

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

Aliases

derived	C₅×SL(2,𝔽₃) ⋊ C₂×C₈
Sylow	C₅ ⋊ C₈×GL(2,𝔽₃)

	subgroup	G/H
center, Frattini, hypercenter	C₂²	AGL(1,𝔽₅)×S₄
commutator, hypocenter	C₅×SL(2,𝔽₃)	C₂×C₈
Fitting	C₂×C₅×Q₈	C₄×D₃
socle	C₂²×C₅	C₄×S₄
prime radical	C₂×C₅×GL(2,𝔽₃)	C₄
cosocle	Dic₅×SL(2,𝔽₃)	C₂²
LCS	G ▷ C₅×SL(2,𝔽₃)
UCS	C₁ ◁ C₂²

254 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.

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

μ_t(G) = 320

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 238092);