#14514948

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, cosocle	C₂×#6732	C₂²
hypocenter	SL(2,𝔽₅)	C₂²⋊C₄
LCS	G ▷ #6732 ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

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

normal subgroups only

This group has 278 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) = 192

Permutation generators:

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

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, 240646);