#14514772

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

Aliases

No aliases for this group.

Splittings

Fitting

C₁₆ ⋊ S₅

Subgroups

	subgroup	G/H
center	C₂	#11751487
commutator, cosocle	C₈×A₅	C₂²
Frattini	C₈	C₂×S₅
Fitting, hypercenter	C₁₆	S₅
socle	C₂×A₅	D₈
hypocenter	A₅	D₁₆
LCS	G ▷ C₈×A₅ ▷ C₄×A₅ ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆

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

normal subgroups only

This group has 174 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) = 80

Permutation generators:

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

Conjugacy classes & character table

49 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240470);