#14514751

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂²

non-solvable

Aliases

No aliases for this group.

Splittings

Fitting

C₄² ⋊ S₅

Subgroups

	subgroup	G/H
center	C₄	C₄⋊S₅
commutator	C₄×A₅	C₂×C₄
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	C₄²	S₅
socle	C₂×A₅	C₂²⋊C₄
prime radical	C₂×C₄⋊S₅	C₂
cosocle	C₂×C₄×A₅	C₂²
hypocenter	A₅	#104
LCS	G ▷ C₄×A₅ ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₄²

332 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 19 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:

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

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240449);