#14514931

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂²

non-solvable

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, socle	C₂²	C₂²⋊S₅
commutator	#6732	C₂×C₄
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	C₂×Q₈	S₅
prime radical	C₂×#91883	C₂
cosocle	C₂×#6732	C₂²
hypocenter	SL(2,𝔽₅)	C₂²⋊C₄
LCS	G ▷ #6732 ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

372 conjugacy classes of subgroups; only the 22 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 22 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:

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

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240629);