#14514995

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	C₄²	S₅
socle	C₂²	C₂×A₅⋊C₄
prime radical	C₂×#6732	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 ◁ C₄²

213 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 213 conjugacy classes of subgroups — too many to draw. Only its 20 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:

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

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, 240693);