#14514962

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

238 conjugacy classes of subgroups; only the 22 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 22 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:

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

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, 240660);