(A₅⋊C₄)⋊C₈ #14514754

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂²

non-solvable

Aliases

unambiguous semidirect product

(A₅⋊C₄)⋊C₈

Subgroups

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

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

normal subgroups only

This group has 291 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) = 96

Permutation generators:

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

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, 240452);