C₂²⋊#91145 #14514951

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

non-solvable

Aliases

unambiguous semidirect product

C₂²⋊#91145

Subgroups

	subgroup	G/H
center, Frattini, cosocle	C₂×C₄	C₂²×A₅
commutator	C₂×SL(2,𝔽₅)	C₂×C₄
Fitting, hypercenter	C₂²⋊C₈	A₅
socle	C₂²	C₂×C₄×A₅
prime radical	C₂²×#6732	C₂
hypocenter	SL(2,𝔽₅)	C₂²⋊C₄
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂×C₄ ◁ C₂²⋊C₈

393 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 393 conjugacy classes of subgroups — too many to draw. Only its 27 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) = 96

Permutation generators:

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

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240649);