C₃×C₁₉×C₈₁ #17987262

order	4617
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 17496
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃

Aliases

abelian

C₃×C₁₉×C₈₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂₇	C₃²×C₁₉
socle, prime radical	C₃²×C₁₉	C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 103
transitive degree	μ_t(G) = 4617

A minimal faithful permutation representation — 2 generators on 103 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81)(85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103);(82,83,84)

Conjugacy classes & character table

4617 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₈₁×#4294, #28353345, #28353346, …
maximal subgroup of	C₉×C₁₉×C₈₁, C₁₉×#10624499, C₁₉×C₃²⋊C₈₁, …
maximal normal subgroup of	C₉×C₁₉×C₈₁, C₁₉×#10624499, C₁₉×C₃²⋊C₈₁, …
maximal quotient of	C₉×C₁₉×C₈₁, C₁₉×C₃²⋊C₈₁, C₁₉×C₉⋊C₈₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4617, 23);

C3×C19×C81 #17987262