C₁₉×#12434 #18018393

order	4864
nilpotency class	4
isoclinism	isoclinic class of #12433
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₉×#12434

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#466
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₉
prime radical	C₂×D₄×C₁₉	D₈
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₄²×C₁₉ ◁ C₈×D₄×C₁₉ ◁ G

230 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 59
transitive degree	μ_t(G) = 2432

A minimal faithful permutation representation — 3 generators on 59 points:

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

Conjugacy classes & character table

703 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 5422);