#14514974

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	#107	A₅
prime radical	C₂×#6732	C₂²
hypocenter	SL(2,𝔽₅)	C₄⋊C₄
LCS	G ▷ #6732 ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

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:

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

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, 240672);