#14515164

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

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, socle	C₂	D₄×S₅
commutator, cosocle	#6732	C₂³
Frattini	C₄	C₂²×S₅
Fitting, hypercenter	SD₁₆	S₅
hypocenter	SL(2,𝔽₅)	C₂×D₄
LCS	G ▷ #6732 ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

426 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 26 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:

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

Conjugacy classes & character table

45 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240862);