C₄⋊#91143 #14514958

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

non-solvable

Aliases

unambiguous semidirect product

C₄⋊#91143

Subgroups

	subgroup	G/H
center, Frattini, socle	C₂³	C₂×S₅
commutator	C₂×SL(2,𝔽₅)	C₂×C₄
Fitting, hypercenter	C₂²×C₄	S₅
prime radical, cosocle	C₂²×SL(2,𝔽₅)	C₂²
hypocenter	SL(2,𝔽₅)	C₄⋊C₄
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

304 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 38 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) = 384

Permutation generators:

(1,3,2,4)(7,30)(8,29)(11,35)(12,36)(13,24)(14,23)(15,33)(16,34)(17,37)(18,38)(21,39)(22,40)(25,42)(26,41)(27,28)(31,32)(43,44)(45,46)(47,50,48,49)(51,52)(53,75)(54,76)(55,56)(57,82)(58,81)(59,69)(60,70)(61,80)(62,79)(63,84)(64,83)(65,66)(67,86)(68,85)(71,87)(72,88);(1,47,2,48)(3,49,4,50)(5,88,14,86,36,52,42,59,40,81,6,87,13,85,35,51,41,60,39,82)(7,61,9,66,18,54,15,56,20,63,8,62,10,65,17,53,16,55,19,64)(11,84,33,71,43,58,38,80,25,90,12,83,34,72,44,57,37,79,26,89)(21,73,31,70,30,68,27,78,24,75,22,74,32,69,29,67,28,77,23,76)(45,92,46,91)

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240656);