#14515007

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
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

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

normal subgroups only

This group has 223 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:

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

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, 240705);