#14514756

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	C₄⋊S₅
commutator	C₄×A₅	C₂×C₄
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	C₂×C₈	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 ◁ C₂×C₈

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

normal subgroups only

This group has 285 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) = 96

Permutation generators:

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

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	SD₁₆×A₅⋊C₄
maximal normal subgroup of	SD₁₆×A₅⋊C₄
maximal quotient of	#72276979

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240454);