#14515039

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	#103	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 ◁ #103

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:

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

Conjugacy classes & character table

63 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#72276859, SD₁₆×#6732
maximal normal subgroup of	SD₁₆×#6732

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240737);