C₁₉×#6878 #17987264

order	4617
nilpotency class	4
isoclinism	isoclinic class of #6878
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

direct product

C₁₉×#6878

Subgroups

	subgroup	G/H
center, socle	C₃×C₁₉	#732
commutator, Frattini, cosocle	C₃×C₉	C₃²×C₁₉
prime radical	C₁₉×#732	C₃
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₉ ◁ C₃²×C₁₉ ◁ C₃×C₉×C₁₉ ◁ G

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 46
transitive degree	μ_t(G) = 513

A minimal faithful permutation representation — 2 generators on 46 points:

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

Conjugacy classes & character table

665 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₁₉⋊C₃×#6878, #28355739, #28355744, …
maximal subgroup of	C₃×C₁₉×#6878, C₁₉×#10624837, C₁₉×#10624838, …
maximal normal subgroup of	C₃×C₁₉×#6878, C₁₉×#10624837, C₁₉×#10624838, …
maximal quotient of	C₁₉×#10624481, C₁₉×#10624483, C₁₉×#10624488, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4617, 25);

C19×#6878 #17987264