C₁₉×#7413 #18013372

order	4864
nilpotency class	5
isoclinism	isoclinic class of #7412
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₉×#7413

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₉	#354
commutator	C₂×C₄²	C₂×C₄×C₁₉
Frattini, cosocle	#391	C₂²×C₁₉
prime radical	C₂³×C₁₉	#99
LCS	G ▷ C₂×C₄² ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#391 ◁ G

178 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 46 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) = 1216

A minimal faithful permutation representation — 2 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)(28,29,31,36,33,38,44,53)(30,39,41,56,40,54,57,52)(32,35,47,51,48,37,45,55)(34,43,49,46,50,58,59,42);(21,24)(22,27)(25,26)(28,30)(29,34,38,50)(31,43)(32,46)(33,40)(35,39,37,54)(36,52,53,56)(41,47)(42,48)(44,58)(45,57)(49,55,59,51)

Conjugacy classes & character table

532 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 401);