#14514929

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂²

non-solvable

Aliases

No aliases for this group.

Subgroups

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

424 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 30 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 192

Permutation generators:

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

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240627);