C₄⋊#91145 #14514972

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

non-solvable

Aliases

unambiguous semidirect product

C₄⋊#91145

Subgroups

	subgroup	G/H
center, Frattini, cosocle	C₂×C₄	C₂²×A₅
commutator	C₂×SL(2,𝔽₅)	C₂×C₄
Fitting, hypercenter	C₄⋊C₈	A₅
socle	C₂²	C₂×C₄×A₅
prime radical	C₂×#6732	C₂²
hypocenter	SL(2,𝔽₅)	C₄⋊C₄
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

266 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 27 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) = 192

Permutation generators:

(1,22,4,17)(2,6,7,12)(3,13,8,19)(5,16,11,10)(9,24,15,18)(14,23,20,21)(25,28,26,27)(29,50,32,45)(30,34,35,40)(31,41,36,47)(33,44,39,38)(37,52,43,46)(42,51,48,49)(53,55,54,56);(1,38,15,40,22,36,10,42,12,47,8,33,14,35,19,32,5,37,7,45,4,44,9,34,17,31,16,48,6,41,3,39,20,30,13,29,11,43,2,50)(18,49,23,46,24,51,21,52)(25,53)(26,54)(27,55)(28,56)

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240670);