#14514733

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

Aliases

No aliases for this group.

Splittings

Fitting

C₂²⋊C₄ ⋊ S₅

Subgroups

	subgroup	G/H
center	C₂	(C₂×S₅)⋊C₄
commutator	C₂²×A₅	C₂×C₄
Frattini	C₂³	C₂×S₅
Fitting, hypercenter	C₂²⋊C₄	S₅
socle	C₂×A₅	C₂²⋊C₄
prime radical	C₂×C₂²⋊S₅	C₂
cosocle	C₂³×A₅	C₂²
hypocenter	A₅	#99
LCS	G ▷ C₂²×A₅ ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂²⋊C₄

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

normal subgroups only

This group has 426 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:

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

Conjugacy classes & character table

43 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240431);