#14515183

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

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center	C₄	D₄×A₅
commutator	#6732	C₂³
Frattini, cosocle	C₄	C₂³×A₅
Fitting, hypercenter	#135	A₅
socle	C₂	C₂×D₄×A₅
hypocenter	SL(2,𝔽₅)	C₂×D₄
LCS	G ▷ #6732 ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #135

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

normal subgroups only

This group has 596 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:

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

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#72276932, #72277090
maximal normal subgroup of	#72277090
maximal quotient of	SD₁₆×#6732

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240881);