#14514807

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂⁵

Aliases

No aliases for this group.

Splittings

Fitting

C₂×D₄ ⋊ S₅

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂²×S₅
commutator, socle, cosocle	C₂²×A₅	C₂³
Fitting, hypercenter	C₂×D₄	S₅
hypocenter	A₅	#120
LCS	G ▷ C₂²×A₅ ▷ A₅
UCS	C₁ ◁ C₂² ◁ C₂×D₄

1177 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 1177 conjugacy classes of subgroups — too many to draw. Only its 37 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) = 40

Permutation generators:

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240505);