#14515004

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

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

normal subgroups only

This group has 222 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:

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

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, 240702);