#14514778

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center	C₂	#11751518
commutator, cosocle	C₈×A₅	C₂²
Frattini	C₈	C₂×S₅
Fitting, hypercenter	Q₁₆	S₅
socle, prime radical	C₂×A₅	D₈
hypocenter	A₅	Q₃₂
LCS	G ▷ C₈×A₅ ▷ C₄×A₅ ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

165 conjugacy classes of subgroups; only the 13 normal subgroups are shown.

normal subgroups only

This group has 165 conjugacy classes of subgroups — too many to draw. Only its 13 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:

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

Conjugacy classes & character table

40 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240476);