#14514996

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₁

non-solvable

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×S₅
commutator	C₂×SL(2,𝔽₅)	C₂×C₄
Fitting, hypercenter	C₄²	S₅
socle	C₂²	C₂×A₅⋊C₄
prime radical	C₂×#6732	C₄
cosocle	C₄×SL(2,𝔽₅)	C₂²
hypocenter	SL(2,𝔽₅)	M₁₆
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

243 conjugacy classes of subgroups; only the 22 normal subgroups are shown.

normal subgroups only

This group has 243 conjugacy classes of subgroups — too many to draw. Only its 22 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:

(1,6,4,7,2,5,3,8)(9,21,30,14,18,26,12,24,31,15,19,27,10,22,29,13,17,25,11,23,32,16,20,28)(33,37,36,40,34,38,35,39)(41,53,62,46,50,58,44,56,63,47,51,59,42,54,61,45,49,57,43,55,64,48,52,60);(1,35,2,36)(3,34,4,33)(5,39,6,40)(7,38,8,37)(9,58,29,44,28,64)(10,57,30,43,27,63)(11,60,31,41,25,61)(12,59,32,42,26,62)(13,55,19,48,22,49)(14,56,20,47,21,50)(15,54,18,45,24,51)(16,53,17,46,23,52)

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240694);