#14514763

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	C₂²⋊S₅
commutator	C₄×A₅	C₂×C₄
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	M₁₆	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 ◁ M₁₆

224 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 19 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:

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240461);