#14515005

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, cosocle	C₂×C₄	C₂²×A₅
commutator	C₂×SL(2,𝔽₅)	C₂×C₄
Fitting, hypercenter	C₄⋊C₈	A₅
socle	C₂²	C₂×C₄×A₅
prime radical	C₂×#6732	C₄
hypocenter	SL(2,𝔽₅)	M₁₆
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

223 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 223 conjugacy classes of subgroups — too many to draw. Only its 25 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:

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

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240703);