#14514941

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

289 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 289 conjugacy classes of subgroups — too many to draw. Only its 20 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) = 96

Permutation generators:

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

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240639);