#14514939

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	C₂²×#6729	C₂
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

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

normal subgroups only

This group has 371 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) = 320

Permutation generators:

(1,48)(2,47)(3,50)(4,49)(5,72,39,66,8,52,26,86,20,53,6,71,40,65,7,51,25,85,19,54)(9,58,24,84,15,56,12,69,38,62,10,57,23,83,16,55,11,70,37,61)(13,68,27,88,17,60,22,74,42,64,14,67,28,87,18,59,21,73,41,63)(29,89,35,79,32,76,43,82,33,77,30,90,36,80,31,75,44,81,34,78)(45,91,46,92);(1,50)(2,49)(3,47)(4,48)(5,59,21,52,14,68)(6,60,22,51,13,67)(7,74,23,81,34,66)(8,73,24,82,33,65)(9,63,25,85,32,75)(10,64,26,86,31,76)(11,88)(12,87)(15,90,37,61,44,83)(16,89,38,62,43,84)(17,71,39,78,29,55)(18,72,40,77,30,56)(19,54,27,70,36,79)(20,53,28,69,35,80)(41,58)(42,57)(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, 240637);