#14514742

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂³

non-solvable

Aliases

No aliases for this group.

Splittings

Fitting

C₄⋊C₄ ⋊ S₅

Subgroups

	subgroup	G/H
center	C₂²	C₂²⋊S₅
commutator	C₄×A₅	C₂×C₄
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	C₄⋊C₄	S₅
socle	C₂²×A₅	D₄
prime radical	C₂×C₄⋊S₅	C₂
cosocle	C₂×C₄×A₅	C₂²
hypocenter	A₅	#102
LCS	G ▷ C₄×A₅ ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

375 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 375 conjugacy classes of subgroups — too many to draw. Only its 23 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:

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

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, 240440);