#14514965

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

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

normal subgroups only

This group has 241 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:

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

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, 240663);