#14514774

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

Aliases

No aliases for this group.

Splittings

Fitting

Q₁₆ ⋊ S₅

Subgroups

	subgroup	G/H
center	C₂	#11751518
commutator, cosocle	C₈×A₅	C₂²
Frattini	C₈	C₂×S₅
Fitting, hypercenter	Q₁₆	S₅
socle	C₂×A₅	D₈
prime radical	#11751487	C₂
hypocenter	A₅	SD₃₂
LCS	G ▷ C₈×A₅ ▷ C₄×A₅ ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

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

normal subgroups only

This group has 176 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) = 80

Permutation generators:

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

Conjugacy classes & character table

40 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240472);