#14514957

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

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center	C₄	D₄×A₅
commutator	#6732	C₂×C₄
Frattini, cosocle	C₂×C₄	C₂²×A₅
Fitting, hypercenter	#104	A₅
socle	C₂	C₂²⋊C₄×A₅
prime radical	#11756696	C₂
hypocenter	SL(2,𝔽₅)	C₂²⋊C₄
LCS	G ▷ #6732 ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #104

353 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 353 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 48
transitive degree	μ_t(G) = 48

Permutation generators:

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

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, 240655);