C₁₉×#6881 #17987267

order	4617
nilpotency class	4
isoclinism	isoclinic class of #6881
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₉ · Schur multiplier (H₂) = C₉

Aliases

direct product

C₁₉×#6881

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

42 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)(22,29,33)(23,28,34)(25,35,31)(26,38,30)(27,40,32)(36,45,43)(37,44,42)(39,46,41);(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×#6881, #28355784, #28355790, …
maximal subgroup of	C₃×C₁₉×#6881, C₁₉×#10624845, C₁₉×#10624846, …
maximal normal subgroup of	C₃×C₁₉×#6881, C₁₉×#10624845, C₁₉×#10624846, …
maximal quotient of	C₁₉×#10624480, C₁₉×#10624481, C₁₉×#10624488, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4617, 28);

C19×#6881 #17987267