#14514950

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, Frattini, socle, cosocle	C₂³	C₂²×A₅
commutator	C₂×SL(2,𝔽₅)	C₂×C₄
Fitting, hypercenter	#95	A₅
prime radical	C₂²×#6732	C₂
hypocenter	SL(2,𝔽₅)	C₂²⋊C₄
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂³ ◁ #95

474 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 37 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:

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

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, 240648);