#14515184

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, socle	C₂	C₂×D₄×A₅
commutator	#6732	C₂³
Frattini, cosocle	C₄	C₂³×A₅
Fitting, hypercenter	#137	A₅
hypocenter	SL(2,𝔽₅)	C₂×D₄
LCS	G ▷ #6732 ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #137

598 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 39 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:

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

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

Relationships

maximal subgroup of

#72277256

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240882);