#14514738

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, prime radical	C₂²×A₅	C₂×C₄
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	C₂×Q₈	S₅
socle	C₂×A₅	C₂²⋊C₄
cosocle	C₂×C₄×A₅	C₂²
hypocenter	A₅	#101
LCS	G ▷ C₂²×A₅ ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

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

normal subgroups only

This group has 337 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) = 80

Permutation generators:

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

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, 240436);