#14514967

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

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

normal subgroups only

This group has 281 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:

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

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, 240665);