A₅⋊#95 #14514721

order	1920
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂⁴

non-solvable

Aliases

unambiguous semidirect product

A₅⋊#95

Subgroups

	subgroup	G/H
center, Frattini	C₂³	C₂×S₅
commutator	C₂×A₅	C₄²
Fitting, hypercenter	C₂²×C₄	S₅
socle, prime radical, cosocle	C₂³×A₅	C₂²
hypocenter	A₅	#95
LCS	G ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

741 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 741 conjugacy classes of subgroups — too many to draw. Only its 45 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) = 96

Permutation generators:

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240419);