#14514923

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	C₂×C₈	S₅
socle	C₂²	C₄×S₅
prime radical, cosocle	C₂×#6732	C₂²
LCS	G ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

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

normal subgroups only

This group has 276 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:

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

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, 240621);