#14514927

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, cosocle	C₂×C₄	C₂²×A₅
commutator, hypocenter	SL(2,𝔽₅)	C₄²
Fitting, hypercenter	#97	A₅
socle	C₂²	C₂×C₄×A₅
prime radical	C₂×#6732	C₂²
LCS	G ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂×C₄ ◁ #97

292 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 33 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) = 192

Permutation generators:

(1,37,13,33,6,36,9,50,5,30,8,48,22,44,2,32,20,47,16,40,4,43,19,39,12,31,15,45,11,35,3,42,17,38,7,29,14,41,10,34)(18,49,23,46,24,51,21,52)(25,54)(26,53)(27,56)(28,55);(1,41,5,51,7,36,19,44,21,34,3,45,10,46,12,29,22,33,24,35,4,47,11,49,2,31,13,38,23,40,8,50,16,52,6,32,17,39,18,30)(9,42,14,43,15,48,20,37)(25,55,26,56)(27,54,28,53)

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240625);