#14514954

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	C₂²⋊C₄×A₅
commutator	C₂×SL(2,𝔽₅)	C₂×C₄
Frattini, cosocle	C₂×C₄	C₂²×A₅
Fitting, hypercenter	#100	A₅
prime radical	C₂×#91881	C₂
hypocenter	SL(2,𝔽₅)	C₂²⋊C₄
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #100

328 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 23 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

A minimal faithful permutation representation — 2 generators on 96 points:

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

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240652);