#14514749

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

non-solvable

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center	C₄	C₂²⋊S₅
commutator	C₄×A₅	C₂×C₄
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	#41	S₅
socle	C₂×A₅	C₂²⋊C₄
prime radical	#41×A₅	C₂
cosocle	C₂×C₄×A₅	C₂²
hypocenter	A₅	#104
LCS	G ▷ C₄×A₅ ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #41

388 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 21 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:

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240447);