C₁₉×#6882 #17987268

order	4617
nilpotency class	4
isoclinism	isoclinic class of #6881
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

direct product

C₁₉×#6882

Subgroups

	subgroup	G/H
center, socle	C₃×C₁₉	#732
commutator, Frattini, cosocle	C₃×C₉	C₃²×C₁₉
prime radical	C₃²×C₁₉	H(3,𝔽₃)
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₉ ◁ C₃²×C₁₉ ◁ C₃×C₉×C₁₉ ◁ G

38 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)(20,21,24,23,28,34,32,27,40)(22,29,33,30,26,38,41,39,46)(25,35,42,37,44,43,36,45,31);(21,25,26,28,37,39,27,36,29)(22,30,41)(24,33,44,40,46,35,34,38,45)(31,43,42)

Conjugacy classes & character table

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

Relationships

Fitting subgroup of	C₁₉⋊C₃×#6882, #28355789, #28355796, …
maximal subgroup of	C₃×C₁₉×#6882, C₁₉×#10624845, C₁₉×#10624847, …
maximal normal subgroup of	C₃×C₁₉×#6882, C₁₉×#10624845, C₁₉×#10624847, …
maximal quotient of	C₁₉×#10624482, C₁₉×#10624483, C₁₉×#10624490, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4617, 29);

C19×#6882 #17987268