#14514735

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

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center	C₂	C₂²⋊(A₅⋊C₄)
commutator	C₂²×A₅	C₂×C₄
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	C₂×D₄	S₅
socle	C₂×A₅	C₂²⋊C₄
prime radical	C₂×D₄×A₅	C₂
cosocle	C₂×C₄×A₅	C₂²
hypocenter	A₅	#100
LCS	G ▷ C₂²×A₅ ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×D₄

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

normal subgroups only

This group has 433 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:

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

Conjugacy classes & character table

43 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240433);