#14514779

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center	C₂	#11751487
commutator, cosocle	C₈×A₅	C₂²
Frattini	C₈	C₂×S₅
Fitting, hypercenter	C₁₆	S₅
socle, prime radical	C₂×A₅	D₈
hypocenter	A₅	Q₃₂
LCS	G ▷ C₈×A₅ ▷ C₄×A₅ ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆

152 conjugacy classes of subgroups; only the 13 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 13 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:

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

Conjugacy classes & character table

49 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240477);