C₂²⋊(A₅⋊C₈) #14514729

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

non-solvable

Aliases

unambiguous semidirect product

C₂²⋊(A₅⋊C₈)

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×S₅
commutator	C₂×A₅	C₂×C₈
Fitting, hypercenter	C₂²×C₄	S₅
socle	C₂²×A₅	C₂×C₄
prime radical	C₂³×A₅	C₄
cosocle	C₂×C₄×A₅	C₂²
hypocenter	A₅	C₂²⋊C₈
LCS	G ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

469 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 469 conjugacy classes of subgroups — too many to draw. Only its 29 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:

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

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, 240427);