C₁₉×#13432 #18019391

order	4864
nilpotency class	4
isoclinism	isoclinic class of #13432
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₉×#13432

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₉	#2044
commutator, Frattini, cosocle	C₂×#41	C₂³×C₁₉
prime radical	C₁₉×#3199	C₂
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂×C₄×C₁₉ ◁ C₂×#41×C₁₉ ◁ G

440 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 86 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)(23,26)(24,37)(25,30)(27,34)(28,35)(29,38)(32,45)(33,48)(36,43)(39,49)(40,50)(41,51)(42,47)(44,46);(21,26)(22,32)(23,35)(27,39)(28,30)(29,40)(31,44)(36,50)(37,43)(41,42)(45,48)(49,51);(20,22,23,33,25,32,35,46)(21,27,28,41,30,42,26,39)(24,34,36,49,38,47,50,51)(29,31,43,44,37,45,40,48)

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, 6420);