#14515006

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	C₄⋊C₄	S₅
hypocenter	SL(2,𝔽₅)	D₈
LCS	G ▷ C₄×SL(2,𝔽₅) ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

227 conjugacy classes of subgroups; only the 16 normal subgroups are shown.

normal subgroups only

This group has 227 conjugacy classes of subgroups — too many to draw. Only its 16 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:

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

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, 240704);