#14514760

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	#107
LCS	G ▷ C₄×A₅ ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

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

normal subgroups only

This group has 277 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:

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

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, 240458);