#14515000

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₁

non-solvable

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×S₅
commutator, prime radical	C₂×SL(2,𝔽₅)	C₂×C₄
Fitting, hypercenter	C₂×C₈	S₅
socle	C₂²	C₄×S₅
cosocle	C₄×SL(2,𝔽₅)	C₂²
hypocenter	SL(2,𝔽₅)	M₁₆
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

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

normal subgroups only

This group has 164 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) = 384

Permutation generators:

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

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240698);