#14514746

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

non-solvable

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center	C₂²	C₂²⋊S₅
commutator	C₄×A₅	C₂×C₄
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	C₄⋊C₄	S₅
socle, prime radical	C₂²×A₅	D₄
cosocle	C₂×C₄×A₅	C₂²
hypocenter	A₅	#103
LCS	G ▷ C₄×A₅ ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

321 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 321 conjugacy classes of subgroups — too many to draw. Only its 23 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:

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240444);