#14514919

order	1920
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₄

non-solvable

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×S₅
commutator, hypocenter	SL(2,𝔽₅)	C₄²
Fitting, hypercenter	C₄²	S₅
socle	C₂²	C₂×A₅⋊C₄
prime radical, cosocle	C₂×#6732	C₂²
LCS	G ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

306 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 26 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:

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

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240617);