#14514946

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

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center	C₄	C₄⋊S₅
commutator	#6732	C₂×C₄
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	C₄²	S₅
socle	C₂	(C₂×S₅)⋊C₄
prime radical	#11756675	C₂
cosocle	C₂×#6732	C₂²
hypocenter	SL(2,𝔽₅)	C₂²⋊C₄
LCS	G ▷ #6732 ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₄²

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

normal subgroups only

This group has 296 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) = 48
transitive degree	μ_t(G) = 48

Permutation generators:

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

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240644);