#14514971

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

non-solvable

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini, socle, cosocle	C₂³	C₂²×A₅
commutator	C₂×SL(2,𝔽₅)	C₂×C₄
Fitting, hypercenter	#95	A₅
prime radical	C₂²×SL(2,𝔽₅)	C₂²
hypocenter	SL(2,𝔽₅)	C₄⋊C₄
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂³ ◁ #95

346 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 37 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:

(1,2)(3,4,5,6)(7,15,14,8,16,13)(9,19,11,10,20,12)(17,30,23,18,29,24)(21,27,25,22,28,26)(31,32)(33,36,35,34)(37,46,44)(38,45,43)(39,50,41)(40,49,42)(47,59,53)(48,60,54)(51,58,55)(52,57,56);(1,31,2,32)(3,33)(4,34)(5,35)(6,36)(7,46,8,45)(9,50,10,49)(11,55,12,56)(13,54,14,53)(15,37,16,38)(17,52,18,51)(19,39,20,40)(21,47,22,48)(23,43,24,44)(25,42,26,41)(27,59,28,60)(29,58,30,57)

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240669);