#14514743

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

non-solvable

Aliases

No aliases for this group.

Splittings

Fitting

C₂×C₈ ⋊ S₅

Subgroups

	subgroup	G/H
center	C₂²	C₄⋊S₅
commutator	C₄×A₅	C₂×C₄
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	C₂×C₈	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 ◁ C₂×C₈

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:

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

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, 240441);