#14514952

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

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, socle	C₂	C₂²⋊C₄×A₅
commutator	C₂×SL(2,𝔽₅)	C₂×C₄
Frattini, cosocle	C₂³	C₂²×A₅
Fitting, hypercenter	#99	A₅
prime radical	C₂×#91881	C₂
hypocenter	SL(2,𝔽₅)	C₂²⋊C₄
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ #99

340 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 23 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:

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

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, 240650);