#14515269

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini, socle, cosocle	C₂²	C₂³×A₅
commutator	C₂×SL(2,𝔽₅)	C₂³
Fitting, hypercenter	C₂²⋊Q₈	A₅
hypocenter	SL(2,𝔽₅)	#41
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂² ◁ C₂²⋊Q₈

496 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 41 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)(5,12,6,11)(7,10,8,9)(13,21,14,22)(15,17,16,18)(19,24,20,23)(25,28,26,27)(29,31)(30,32)(33,40,34,39)(35,38,36,37)(41,49,42,50)(43,45,44,46)(47,52,48,51)(53,56,54,55);(1,4,2,3)(5,22,15,20,14,17,6,21,16,19,13,18)(7,27,12,26,9,23,8,28,11,25,10,24)(29,31,30,32)(33,49,43,47,42,46,34,50,44,48,41,45)(35,56,40,53,37,52,36,55,39,54,38,51);(1,29,2,30)(3,31,4,32)(5,33,6,34)(7,35,8,36)(9,37,10,38)(11,39,12,40)(13,41,14,42)(15,43,16,44)(17,45,18,46)(19,47,20,48)(21,49,22,50)(23,51,24,52)(25,53,26,54)(27,55,28,56)

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, 240967);