#14514757

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	#106
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:

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

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, 240455);