#14515212

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

non-solvable

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center	C₂×C₄	C₂×S₅
commutator, cosocle	C₂×SL(2,𝔽₅)	C₂³
Frattini, socle	C₂²	C₂²×S₅
Fitting, hypercenter	C₄²	S₅
prime radical	#11751514	C₂
hypocenter	SL(2,𝔽₅)	#41
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

370 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 28 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:

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

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, 240910);