C₁₉×#6879 #17987265

order	4617
nilpotency class	4
isoclinism	isoclinic class of #6878
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₉ · Schur multiplier (H₂) = C₃×C₉

Aliases

direct product

C₁₉×#6879

Subgroups

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

48 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)(22,26,31)(23,27,34)(25,35,40)(28,38,42)(29,36,32)(30,39,33)(37,44,46)(41,45,43);(21,25,36,27,37,45,39,38,26)(24,31,42,33,43,44,34,32,35)

Conjugacy classes & character table

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

Relationships

Fitting subgroup of	#28353468, #28353472, #28353475, …
maximal subgroup of	C₁₉×#10624535, C₁₉×#10624537, C₁₉×#10624538, …
maximal normal subgroup of	C₁₉×#10624535, C₁₉×#10624537, C₁₉×#10624538, …
maximal quotient of	C₁₉×#10624480, C₁₉×#10624489, C₁₉×#10624494, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4617, 26);

C19×#6879 #17987265