#14515293

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini, socle, cosocle	C₂	C₂⁴×A₅
commutator, hypocenter	SL(2,𝔽₅)	C₂⁴
Fitting, hypercenter	2₋¹⁺⁴	A₅
LCS	G ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂ ◁ 2₋¹⁺⁴

2036 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 2036 conjugacy classes of subgroups — too many to draw. Only its 135 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) = 96
transitive degree	μ_t(G) = 96

Permutation generators:

(49,50)(51,56)(52,60)(53,65)(54,67)(55,69)(57,73)(58,75)(59,77)(61,80)(62,84)(63,85)(64,79)(66,68)(70,88)(71,90)(72,92)(74,76)(78,81)(82,94)(83,93)(86,96)(87,98)(89,91)(95,97)(99,100);(1,17,6,4)(2,13,39,48,12,25,3,42,47,44,10,35,41,37,34,8,15,22,45,32)(5,16,19,18)(7,46,28,9,11,40,38,33,24,14,23,36,31,27,30,21,20,43,26,29)(51,67,56,54)(52,63,89,98,62,75,53,92,97,94,60,85,91,87,84,58,65,72,95,82)(55,66,69,68)(57,96,78,59,61,90,88,83,74,64,73,86,81,77,80,71,70,93,76,79);(1,41,20,16,7,45,6,39,38,18,23,47)(2,12,30,24,31,15,10,34,11,26,28,3)(4,22,36,19,21,48,17,42,46,5,40,37)(8,44,14,27,33,13,25,32,29,9,43,35)(51,91,70,66,57,95,56,89,88,68,73,97)(52,62,80,74,81,65,60,84,61,76,78,53)(54,72,86,69,71,98,67,92,96,55,90,87)(58,94,64,77,83,63,75,82,79,59,93,85);(1,51)(2,52)(3,53)(4,54)(5,55)(6,56)(7,57)(8,58)(9,59)(10,60)(11,61)(12,62)(13,63)(14,64)(15,65)(16,66)(17,67)(18,68)(19,69)(20,70)(21,71)(22,72)(23,73)(24,74)(25,75)(26,76)(27,77)(28,78)(29,79)(30,80)(31,81)(32,82)(33,83)(34,84)(35,85)(36,86)(37,87)(38,88)(39,89)(40,90)(41,91)(42,92)(43,93)(44,94)(45,95)(46,96)(47,97)(48,98)(49,99)(50,100)

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#72277309
maximal normal subgroup of	#72277309

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240991);