#14514943

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	(C₂×S₅)⋊C₄
commutator	C₂×SL(2,𝔽₅)	C₂×C₄
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	M₁₆	S₅
prime radical, cosocle	C₂×#6732	C₂²
hypocenter	SL(2,𝔽₅)	C₂²⋊C₄
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

267 conjugacy classes of subgroups; only the 18 normal subgroups are shown.

normal subgroups only

This group has 267 conjugacy classes of subgroups — too many to draw. Only its 18 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:

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

Conjugacy classes & character table

42 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240641);