#14514973

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

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	#106	A₅
prime radical	C₂×#6732	C₂²
hypocenter	SL(2,𝔽₅)	C₄⋊C₄
LCS	G ▷ #6732 ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

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

normal subgroups only

This group has 240 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:

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

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, 240671);