#14514882

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

Aliases

No aliases for this group.

Splittings

Fitting

D₈ ⋊ S₅

Subgroups

	subgroup	G/H
center	C₂	D₄×S₅
commutator, cosocle	C₄×A₅	C₂³
Frattini	C₄	C₂²×S₅
Fitting, hypercenter	D₈	S₅
socle	C₂×A₅	C₂×D₄
hypocenter	A₅	AGL(1,ℤ/8)
LCS	G ▷ C₄×A₅ ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

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

normal subgroups only

This group has 518 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:

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

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, 240580);