#14515160

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

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, socle	C₂	D₄×S₅
commutator, cosocle	#6732	C₂³
Frattini	C₄	C₂²×S₅
Fitting, hypercenter	SD₁₆	S₅
hypocenter	SL(2,𝔽₅)	C₂×D₄
LCS	G ▷ #6732 ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

417 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 417 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.

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

Full subgroup data →

Presentation

minimal degree	μ(G) = 96
transitive degree	μ_t(G) = 96

Permutation generators:

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

Conjugacy classes & character table

39 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240858);