#14515294

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini, socle, cosocle	C₂	C₂⁴×A₅
commutator, hypocenter	SL(2,𝔽₅)	C₂⁴
Fitting, hypercenter	H(5,𝔽₂)	A₅
LCS	G ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂ ◁ H(5,𝔽₂)

2010 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 2010 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 96
transitive degree	μ_t(G) = 96

Permutation generators:

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

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240992);