#14514964

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, 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)	C₄⋊C₄
LCS	G ▷ #6732 ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

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

normal subgroups only

This group has 249 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)(3,6,16,12,20,24,7,14,25,22,10,17,4,5,15,11,19,23,8,13,26,21,9,18)(27,28)(29,51,37,49,35,32,34,42,48,43,45,39,30,52,38,50,36,31,33,41,47,44,46,40);(1,27,2,28)(3,45,11,51,10,32,17,37,25,49,4,46,12,52,9,31,18,38,26,50)(5,30,6,29)(7,35,21,41,19,40,23,47,15,44,8,36,22,42,20,39,24,48,16,43)(13,34,14,33)

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, 240662);