#14514955

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

non-solvable

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, socle	C₂²	D₄×A₅
commutator	#6732	C₂×C₄
Frattini, cosocle	C₂×C₄	C₂²×A₅
Fitting, hypercenter	#103	A₅
prime radical	C₂×#91883	C₂
hypocenter	SL(2,𝔽₅)	C₂²⋊C₄
LCS	G ▷ #6732 ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

347 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 347 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.

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

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 192

Permutation generators:

(1,54,2,53)(3,56,4,55)(5,94,28,71,41,97,20,75,46,57,24,80,6,93,27,72,42,98,19,76,45,58,23,79)(7,95,26,70,44,100,17,73,47,59,22,78,8,96,25,69,43,99,18,74,48,60,21,77)(9,87,16,83,36,89,32,101,38,61,50,68,10,88,15,84,35,90,31,102,37,62,49,67)(11,86,14,82,33,92,29,103,39,63,52,66,12,85,13,81,34,91,30,104,40,64,51,65);(1,55)(2,56)(3,54)(4,53)(5,66,42,60,15,96,6,65,41,59,16,95)(7,68,43,57,14,94,8,67,44,58,13,93)(9,85,47,64,36,98,10,86,48,63,35,97)(11,87,45,61,33,99,12,88,46,62,34,100)(17,89,21,71,39,76,18,90,22,72,40,75)(19,91,24,70,38,74,20,92,23,69,37,73)(25,81,50,80,31,104,26,82,49,79,32,103)(27,84,51,77,29,102,28,83,52,78,30,101)

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240653);