#14514944

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

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, socle	C₂	(C₂×S₅)⋊C₄
commutator	C₂×SL(2,𝔽₅)	C₂×C₄
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	M₁₆	S₅
prime radical	C₂×#91872	C₂
cosocle	C₂×#6732	C₂²
hypocenter	SL(2,𝔽₅)	C₂²⋊C₄
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

297 conjugacy classes of subgroups; only the 18 normal subgroups are shown.

normal subgroups only

This group has 297 conjugacy classes of subgroups — too many to draw. Only its 18 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) = 80
transitive degree	μ_t(G) = 80

Permutation generators:

(1,75,43,83,15,78,26,95,31,96,12,62,29,73,8,65,13,89,18,92,5,55,16,71,39,59,6,80,20,81,2,52,9,85,28,58,3,67,42,69)(4,60,35,91,22,51,10,79,32,88,7,49,37,57,24,54,11,90,41,86,14,50,23,64,34,61,17,68,47,84,27,53,25,77,45,74,30,66,19,94)(21,87,33,56,44,63,48,76)(36,93,38,82,40,72,46,70);(1,77)(2,91)(3,94)(4,73)(5,57)(6,88)(7,83)(8,53)(9,87)(10,81)(11,92)(12,64)(13,86)(14,85)(15,60)(16,56)(17,96)(18,51)(19,59)(20,74)(21,95)(22,55)(23,93)(24,62)(25,70)(26,84)(27,71)(28,49)(29,63)(30,69)(31,54)(32,65)(33,67)(34,75)(35,72)(36,90)(37,82)(38,79)(39,50)(40,66)(41,78)(42,61)(43,76)(44,80)(45,52)(46,68)(47,58)(48,89)

Conjugacy classes & character table

42 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240642);