#14514959

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

non-solvable

Aliases

No aliases for this group.

Subgroups

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

280 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 30 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) = 384

Permutation generators:

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

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, 240657);