#14514771

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

Aliases

No aliases for this group.

Splittings

Fitting

D₈ ⋊ S₅

Subgroups

	subgroup	G/H
center	C₂	#11751518
commutator, cosocle	C₈×A₅	C₂²
Frattini	C₈	C₂×S₅
Fitting, hypercenter	D₈	S₅
socle	C₂×A₅	D₈
hypocenter	A₅	D₁₆
LCS	G ▷ C₈×A₅ ▷ C₄×A₅ ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₈

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

normal subgroups only

This group has 194 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:

(1,3,2)(4,5)(6,35,10,32,9,36,13,30,7,34,11,33,8,37,12,31)(14,23,18,27,17,24,21,28,15,22,19,26,16,25,20,29);(1,3,5,2)(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, 240469);