#14515214

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

non-solvable

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center	C₂×C₄	C₂×S₅
commutator, cosocle	C₂×SL(2,𝔽₅)	C₂³
Frattini, socle	C₂²	C₂²×S₅
Fitting, hypercenter	C₂²×C₄	S₅
prime radical	C₂²×SL(2,𝔽₅)	C₂²
hypocenter	SL(2,𝔽₅)	#41
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

364 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 36 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:

(1,5,18)(2,10,24)(3,15,6)(4,20,12)(7,8,23)(9,13,14)(11,19,16)(17,21,22)(25,29,42)(26,34,48)(27,39,30)(28,44,36)(31,32,47)(33,37,38)(35,43,40)(41,45,46)(49,51,50,52)(53,57,70)(54,62,76)(55,67,58)(56,72,64)(59,60,75)(61,65,66)(63,71,68)(69,73,74)(77,81,94)(78,86,100)(79,91,82)(80,96,88)(83,84,99)(85,89,90)(87,95,92)(93,97,98)(101,103,102,104);(1,44,23,31,24,46,3,34,11,43,12,38)(2,29,9,37,6,32,4,39,17,45,18,40)(5,47,13,48,8,27,15,35,21,36,16,25)(7,42,22,26,10,33,19,30,14,28,20,41)(53,96,75,83,76,98,55,86,63,95,64,90)(54,81,61,89,58,84,56,91,69,97,70,92)(57,99,65,100,60,79,67,87,73,88,68,77)(59,94,74,78,62,85,71,82,66,80,72,93)(101,102)(103,104);(1,53)(2,54)(3,55)(4,56)(5,57)(6,58)(7,59)(8,60)(9,61)(10,62)(11,63)(12,64)(13,65)(14,66)(15,67)(16,68)(17,69)(18,70)(19,71)(20,72)(21,73)(22,74)(23,75)(24,76)(25,77)(26,78)(27,79)(28,80)(29,81)(30,82)(31,83)(32,84)(33,85)(34,86)(35,87)(36,88)(37,89)(38,90)(39,91)(40,92)(41,93)(42,94)(43,95)(44,96)(45,97)(46,98)(47,99)(48,100)(49,101)(50,102)(51,103)(52,104)

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, 240912);