#14514966

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

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center	C₄	C₂²⋊S₅
commutator	#6732	C₂×C₄
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	M₁₆	S₅
socle	C₂	(A₅⋊C₄)⋊C₄
prime radical, cosocle	C₂×#6732	C₂²
hypocenter	SL(2,𝔽₅)	C₄⋊C₄
LCS	G ▷ #6732 ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ M₁₆

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

normal subgroups only

This group has 226 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:

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

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, 240664);