#14515003

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, cosocle	C₂×C₄	C₂²×A₅
commutator	C₂×SL(2,𝔽₅)	C₂×C₄
Fitting, hypercenter	#97	A₅
socle	C₂²	C₂×C₄×A₅
prime radical	C₂×#6732	C₄
hypocenter	SL(2,𝔽₅)	M₁₆
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂×C₄ ◁ #97

249 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 249 conjugacy classes of subgroups — too many to draw. Only its 27 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:

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

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240701);