#14515009

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

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, socle	C₂²	C₂²⋊S₅
commutator, cosocle	C₄×SL(2,𝔽₅)	C₂²
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	C₂×D₄	S₅
prime radical	D₄×SL(2,𝔽₅)	C₂
hypocenter	SL(2,𝔽₅)	D₈
LCS	G ▷ C₄×SL(2,𝔽₅) ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₄

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

normal subgroups only

This group has 199 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

transitive degree

μ_t(G) = 192

Permutation generators:

(1,6,4,7,2,5,3,8)(9,32,20,21,26,13,12,30,18,24,27,16,10,31,19,22,25,14,11,29,17,23,28,15)(33,40,35,37,34,39,36,38)(41,61,51,56,58,47,43,63,50,53,60,46,42,62,52,55,57,48,44,64,49,54,59,45);(1,34)(2,33)(3,36)(4,35)(5,38)(6,37)(7,40)(8,39)(9,56,13,50,30,42,23,46,17,61)(10,55,14,49,29,41,24,45,18,62)(11,53,15,52,32,44,22,48,19,63)(12,54,16,51,31,43,21,47,20,64)(25,58)(26,57)(27,60)(28,59)

Conjugacy classes & character table

45 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240707);