#14514747

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	#103
LCS	G ▷ C₄×A₅ ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

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:

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

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240445);