(C₂×S₅)⋊C₈ #14514730

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂³

non-solvable

Aliases

unambiguous semidirect product

(C₂×S₅)⋊C₈

Splittings

Fitting

C₂×C₈ ⋊ S₅

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×S₅
commutator	C₂×A₅	C₂×C₈
Fitting, hypercenter	C₂×C₈	S₅
socle	C₂²×A₅	C₂×C₄
prime radical	C₂²×S₅	C₄
cosocle	C₂×C₄×A₅	C₂²
hypocenter	A₅	C₂²⋊C₈
LCS	G ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

377 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 377 conjugacy classes of subgroups — too many to draw. Only its 25 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:

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

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240428);