C₁₉×#13350 #18019309

order	4864
nilpotency class	4
isoclinism	isoclinic class of #13350
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₉×#13350

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2021
commutator, Frattini, cosocle	C₂×#41	C₂³×C₁₉
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

738 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 51
transitive degree	μ_t(G) = 608

A minimal faithful permutation representation — 3 generators on 51 points:

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

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, 6338);