#14514945

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

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, socle	C₂	(C₂×S₅)⋊C₄
commutator	C₂×SL(2,𝔽₅)	C₂×C₄
Frattini	C₂³	C₂×S₅
Fitting, hypercenter	C₂²⋊C₄	S₅
prime radical	C₂×#91877	C₂
cosocle	C₂²×SL(2,𝔽₅)	C₂²
hypocenter	SL(2,𝔽₅)	C₂²⋊C₄
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂²⋊C₄

277 conjugacy classes of subgroups; only the 18 normal subgroups are shown.

normal subgroups only

This group has 277 conjugacy classes of subgroups — too many to draw. Only its 18 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:

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

Conjugacy classes & character table

42 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240643);