#14514998

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	C₂×C₈	S₅
socle	C₂²	C₄×S₅
prime radical	C₂×#6729	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 ◁ C₂×C₈

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

normal subgroups only

This group has 185 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) = 320

Permutation generators:

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

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, 240696);