#14515049

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	C₂×SL(2,𝔽₅)	D₄
hypocenter	SL(2,𝔽₅)	Q₁₆
LCS	G ▷ C₄×SL(2,𝔽₅) ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

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

normal subgroups only

This group has 204 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) = 384

Permutation generators:

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

Conjugacy classes & character table

63 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240747);