#14514942

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂²

non-solvable

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, socle	C₂²	C₂²⋊S₅
commutator	#6732	C₂×C₄
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	C₄⋊C₄	S₅
prime radical	C₂×#91872	C₂
cosocle	C₂×#6732	C₂²
hypocenter	SL(2,𝔽₅)	C₂²⋊C₄
LCS	G ▷ #6732 ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

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

normal subgroups only

This group has 327 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) = 96

Permutation generators:

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

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240640);