C₂²⋊#91143 #14514928

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂²

non-solvable

Aliases

unambiguous semidirect product

C₂²⋊#91143

Subgroups

	subgroup	G/H
center, Frattini, socle	C₂³	C₂×S₅
commutator	C₂×SL(2,𝔽₅)	C₂×C₄
Fitting, hypercenter	C₂⁴	S₅
prime radical	C₂³×SL(2,𝔽₅)	C₂
cosocle	C₂²×SL(2,𝔽₅)	C₂²
hypocenter	SL(2,𝔽₅)	C₂²⋊C₄
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂³ ◁ C₂⁴

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

normal subgroups only

This group has 434 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) = 192

Permutation generators:

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

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, 240626);