#14514979

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

non-solvable

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×S₅
commutator, hypocenter	SL(2,𝔽₅)	C₂×C₈
Fitting, hypercenter	C₂²×C₄	S₅
socle	C₂²	C₂×A₅⋊C₄
prime radical	C₂²×SL(2,𝔽₅)	C₄
cosocle	C₄×SL(2,𝔽₅)	C₂²
LCS	G ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

226 conjugacy classes of subgroups; only the 24 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 24 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:

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

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240677);