#14514883

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Splittings

Fitting

SD₁₆ ⋊ S₅

Subgroups

	subgroup	G/H
center	C₂	D₄×S₅
commutator, cosocle	C₄×A₅	C₂³
Frattini	C₄	C₂²×S₅
Fitting, hypercenter	SD₁₆	S₅
socle	C₂×A₅	C₂×D₄
hypocenter	A₅	AGL(1,ℤ/8)
LCS	G ▷ C₄×A₅ ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

507 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 507 conjugacy classes of subgroups — too many to draw. Only its 27 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) = 40

Permutation generators:

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

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, 240581);