#14514969

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

non-solvable

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×S₅
commutator	C₂×SL(2,𝔽₅)	C₂×C₄
Fitting, hypercenter	C₂×C₈	S₅
socle	C₂²	C₄×S₅
prime radical, cosocle	C₂×#6732	C₂²
hypocenter	SL(2,𝔽₅)	C₄⋊C₄
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

239 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 239 conjugacy classes of subgroups — too many to draw. Only its 20 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) = 96

Permutation generators:

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

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, 240667);