#14514876

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	#135
LCS	G ▷ C₄×A₅ ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

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

normal subgroups only

This group has 465 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) = 48

Permutation generators:

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

Conjugacy classes & character table

49 conjugacy classes — view the full character table.

Relationships

maximal quotient of

SD₁₆×A₅⋊C₄

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240574);