#14514739

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center	C₂	(C₂×S₅)⋊C₄
commutator, prime radical	C₂²×A₅	C₂×C₄
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	M₁₆	S₅
socle	C₂×A₅	C₂²⋊C₄
cosocle	C₂×C₄×A₅	C₂²
hypocenter	A₅	#101
LCS	G ▷ C₂²×A₅ ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

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

normal subgroups only

This group has 286 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) = 48

Permutation generators:

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

Conjugacy classes & character table

43 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240437);