C₁₉×#6869 #17987255

order	4617
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₃×C₉×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

direct product

C₁₉×#6869

Subgroups

	subgroup	G/H
center	C₉×C₁₉	H(3,𝔽₃)
commutator	C₃²	C₃×C₉×C₁₉
Frattini, cosocle	C₃×C₉	C₃²×C₁₉
socle	C₃×C₁₉	C₃²⋊C₉
prime radical	C₃³×C₁₉	C₉
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₉×C₁₉ ◁ C₃×C₉×C₁₉ ◁ G

62 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)(20,21,24,22,27,32,28,36,40,23,25,31,29,33,39,37,41,45,30,26,34,38,35,42,44,43,46);(21,25,26)(27,33,35)(36,41,43)

Conjugacy classes & character table

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

Relationships

Fitting subgroup of	#28353366, #28353367, #28353376, …
maximal subgroup of	C₁₉×#10624507, C₁₉×#10624510, C₁₉×#10624511, …
maximal normal subgroup of	C₁₉×#10624507, C₁₉×#10624510, C₁₉×#10624511, …
maximal quotient of	C₁₉×#10624444, C₁₉×#10624445, C₁₉×#10624446, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4617, 16);

C19×#6869 #17987255