#14514947

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

non-solvable

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, socle	C₂²	C₄⋊S₅
commutator	#6732	C₂×C₄
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	C₂×C₈	S₅
prime radical	C₂×#91872	C₂
cosocle	C₂×#6732	C₂²
hypocenter	SL(2,𝔽₅)	C₂²⋊C₄
LCS	G ▷ #6732 ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

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

normal subgroups only

This group has 308 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

transitive degree

μ_t(G) = 160

Permutation generators:

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

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, 240645);