#14515101

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

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini, socle	C₂²	C₂²×S₅
commutator, cosocle	C₂×SL(2,𝔽₅)	C₂³
Fitting, hypercenter	C₂²×C₄	S₅
prime radical	C₂²×#6732	C₂
hypocenter	SL(2,𝔽₅)	C₂×D₄
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂² ◁ C₂²×C₄

553 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 553 conjugacy classes of subgroups — too many to draw. Only its 32 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) = 96

Permutation generators:

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

54 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240799);