#14514809

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂⁵

Aliases

No aliases for this group.

Splittings

Fitting

C₂⁴ ⋊ S₅

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂²×S₅
commutator, socle, cosocle	C₂²×A₅	C₂³
Fitting, hypercenter	C₂⁴	S₅
hypocenter	A₅	#120
LCS	G ▷ C₂²×A₅ ▷ A₅
UCS	C₁ ◁ C₂² ◁ C₂⁴

1528 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 1528 conjugacy classes of subgroups — too many to draw. Only its 41 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) = 40

Permutation generators:

(1,5,3,2)(6,30,8,32)(7,31,9,33)(10,35,12,37)(11,34,13,36)(14,24,16,22)(15,25,17,23)(18,29,20,27)(19,28,21,26);(1,4)(2,3,5)(6,36,9,35)(7,37,8,34)(10,33,13,30)(11,32,12,31)(14,26,17,29)(15,27,16,28)(18,23,21,24)(19,22,20,25);(1,4,2,3)(6,25)(7,24)(8,23)(9,22)(10,28)(11,29)(12,26)(13,27)(14,31)(15,30)(16,33)(17,32)(18,34)(19,35)(20,36)(21,37)

Conjugacy classes & character table

58 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240507);