#14514741

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂³

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	C₂×D₄	S₅
socle	C₂²×A₅	D₄
prime radical	C₂×D₄×A₅	C₂
cosocle	C₂×C₄×A₅	C₂²
hypocenter	A₅	#102
LCS	G ▷ C₄×A₅ ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₄

467 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 467 conjugacy classes of subgroups — too many to draw. Only its 25 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:

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	SD₁₆×A₅⋊C₄
maximal normal subgroup of	SD₁₆×A₅⋊C₄
maximal quotient of	#72276971

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240439);