#14514775

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

Aliases

No aliases for this group.

Subgroups

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

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

normal subgroups only

This group has 183 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:

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

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, 240473);