#14514840

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Splittings

Fitting

C₄² ⋊ S₅

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂²×S₅
commutator, socle, cosocle	C₂²×A₅	C₂³
Fitting, hypercenter	C₄²	S₅
prime radical	C₂²×S₅	C₂²
hypocenter	A₅	#126
LCS	G ▷ C₂²×A₅ ▷ A₅
UCS	C₁ ◁ C₂² ◁ C₄²

470 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 29 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:

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

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240538);