#14514936

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⋊(A₅⋊C₄)
commutator	C₂×SL(2,𝔽₅)	C₂×C₄
Frattini	C₂³	C₂×S₅
Fitting, hypercenter	C₂×D₄	S₅
prime radical	C₂×#91881	C₂
cosocle	C₂²×SL(2,𝔽₅)	C₂²
hypocenter	SL(2,𝔽₅)	C₂²⋊C₄
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂×D₄

338 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 20 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:

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

Conjugacy classes & character table

42 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240634);