#14514794

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

non-solvable

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂²×S₅
commutator	C₂×A₅	C₂²×C₄
Fitting, hypercenter	C₂²⋊C₄	S₅
socle, cosocle	C₂²×A₅	C₂³
prime radical	C₂³×A₅	C₂²
hypocenter	A₅	#117
LCS	G ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂² ◁ C₂²⋊C₄

665 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 665 conjugacy classes of subgroups — too many to draw. Only its 41 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) = 48

Permutation generators:

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

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240492);