#14514997

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₁

non-solvable

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×S₅
commutator	C₂×SL(2,𝔽₅)	C₂×C₄
Fitting, hypercenter	C₂²×C₄	S₅
socle	C₂²	C₂×A₅⋊C₄
prime radical	C₂²×SL(2,𝔽₅)	C₄
cosocle	C₄×SL(2,𝔽₅)	C₂²
hypocenter	SL(2,𝔽₅)	M₁₆
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

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

normal subgroups only

This group has 234 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:

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

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, 240695);