#14515028

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₁

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
prime radical	C₄⋊#6732	C₂
hypocenter	SL(2,𝔽₅)	SD₁₆
LCS	G ▷ C₄×SL(2,𝔽₅) ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

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

normal subgroups only

This group has 198 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:

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

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, 240726);