#14514925

order	1920
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₄

non-solvable

Aliases

No aliases for this group.

Splittings

derived

SL(2,𝔽₅) ⋊ C₄²

Subgroups

	subgroup	G/H
center, Frattini, socle, cosocle	C₂³	C₂²×A₅
commutator, hypocenter	SL(2,𝔽₅)	C₄²
Fitting, hypercenter	#95	A₅
prime radical	C₂²×SL(2,𝔽₅)	C₂²
LCS	G ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂³ ◁ #95

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

normal subgroups only

This group has 348 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) = 384

Permutation generators:

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

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240623);