#14515271

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini, socle, cosocle	C₂²	C₂³×A₅
commutator	C₂×SL(2,𝔽₅)	C₂³
Fitting, hypercenter	#126	A₅
hypocenter	SL(2,𝔽₅)	#41
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂² ◁ #126

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

normal subgroups only

This group has 479 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) = 192

Permutation generators:

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

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, 240969);