#14515041

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, socle	C₂²	D₄×A₅
commutator	C₄×SL(2,𝔽₅)	C₂²
Frattini, cosocle	C₂×C₄	C₂²×A₅
Fitting, hypercenter	#106	A₅
prime radical	C₄⋊#6732	C₂
hypocenter	SL(2,𝔽₅)	SD₁₆
LCS	G ▷ C₄×SL(2,𝔽₅) ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

228 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 21 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:

(1,33,4,36)(2,34,8,40)(3,47,16,54,13,35,14,48,23,45,9,46,21,55,7,41,15,53,22,39)(5,44,18,56,11,37,17,50,20,43,6,49,19,52,10,38,12,51,24,42)(25,58)(26,57)(27,60)(28,59)(29,62)(30,61)(31,64)(32,63);(1,55,12,50,9,33,22,44,19,41,4,54,17,51,3,36,23,49,18,35)(2,52,14,53,6,34,24,46,16,38,8,56,15,48,5,40,20,47,21,37)(7,39,13,45)(10,42,11,43)(25,61,26,62)(27,63,28,64)(29,59,30,60)(31,58,32,57)

Conjugacy classes & character table

63 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	SD₁₆×#6732
maximal normal subgroup of	SD₁₆×#6732

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240739);