#14514994

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

228 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 28 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:

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

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, 240692);