#14514762

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

non-solvable

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center	C₄	C₄⋊S₅
commutator	C₄×A₅	C₂×C₄
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	C₂×C₈	S₅
socle	C₂×A₅	C₄⋊C₄
prime radical	C₂²×A₅	Q₈
cosocle	C₂×C₄×A₅	C₂²
hypocenter	A₅	#108
LCS	G ▷ C₄×A₅ ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈

233 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 233 conjugacy classes of subgroups — too many to draw. Only its 21 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) = 80

Permutation generators:

(1,4,5)(2,3)(6,34,9,37,7,35,8,36)(10,30,13,33,11,31,12,32)(14,27,17,28,15,26,16,29)(18,23,21,24,19,22,20,25);(1,4,3,5,2)(6,19,11,15,7,18,10,14)(8,21,13,17,9,20,12,16)(22,35,27,31,23,34,26,30)(24,37,29,33,25,36,28,32)

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240460);