C₁₉×#6875 #17987261

order	4617
nilpotency class	3
isoclinism	isoclinic class of #6875
automorphism	?
homology	Abelianization (H₁) = C₃×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₉×#6875

Subgroups

	subgroup	G/H
center, socle	C₃×C₁₉	C₉⋊C₉
commutator	C₉	C₃×C₉×C₁₉
Frattini, cosocle	C₃×C₉	C₃²×C₁₉
prime radical	C₃²×C₁₉	3₋¹⁺²
LCS	G ▷ C₉ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₁₉ ◁ C₃×C₉×C₁₉ ◁ G

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

Conjugacy classes & character table

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

Relationships

Fitting subgroup of	C₁₉⋊C₃×#6875, #28354740, #28355707, …
maximal subgroup of	C₃×C₁₉×#6875, C₁₉×#10624709, C₁₉×#10624828, …
maximal normal subgroup of	C₃×C₁₉×#6875, C₁₉×#10624709, C₁₉×#10624828, …
maximal quotient of	C₁₉×#10624462, C₁₉×#10624472, C₃×C₁₉×#6875

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4617, 22);

C19×#6875 #17987261