#14514938

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

non-solvable

Aliases

No aliases for this group.

Subgroups

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

317 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 317 conjugacy classes of subgroups — too many to draw. Only its 30 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) = 384

Permutation generators:

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

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, 240636);