#14514968

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

non-solvable

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini, socle	C₂³	C₂×S₅
commutator	C₂×SL(2,𝔽₅)	C₂×C₄
Fitting, hypercenter	C₂²×C₄	S₅
prime radical, cosocle	C₂²×SL(2,𝔽₅)	C₂²
hypocenter	SL(2,𝔽₅)	C₄⋊C₄
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

281 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 281 conjugacy classes of subgroups — too many to draw. Only its 30 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) = 384

Permutation generators:

(1,3,2,4)(5,35,34,37,27,7)(6,36,33,38,28,8)(9,30,43,25,39,13)(10,29,44,26,40,14)(11,24,31)(12,23,32)(15,21)(16,22)(17,19,41,18,20,42)(45,46)(47,50,48,49)(51,81,80,83,73,53)(52,82,79,84,74,54)(55,76,89,71,85,59)(56,75,90,72,86,60)(57,70,77)(58,69,78)(61,67)(62,68)(63,65,87,64,66,88)(91,92);(1,48)(2,47)(3,50)(4,49)(5,58)(6,57)(7,68)(8,67)(9,70)(10,69)(11,51)(12,52)(13,72)(14,71)(15,76)(16,75)(17,74)(18,73)(19,78)(20,77)(21,53)(22,54)(23,55)(24,56)(25,59)(26,60)(27,63)(28,64)(29,61)(30,62)(31,65)(32,66)(33,85)(34,86)(35,83)(36,84)(37,82)(38,81)(39,80)(40,79)(41,90)(42,89)(43,87)(44,88)(45,92,46,91)

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, 240666);