C₁₉×#732 #13095294

order	1539
nilpotency class	3
isoclinism	isoclinic class of AΣL(1,𝔽₂₇)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₉ · Schur multiplier (H₂) = C₃²

Aliases

direct product

C₁₉×#732

Subgroups

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

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

Conjugacy classes & character table

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

Relationships

Fitting subgroup of	#28356807, #28356810, #28356813, …
maximal subgroup of	C₁₉×#6878, C₁₉×#6879, C₁₉×#6881, …
maximal normal subgroup of	C₁₉×#6878, C₁₉×#6879, C₁₉×#6881, …
maximal quotient of	C₁₉×#6856, C₁₉×#6859, C₁₉×#6861, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1539, 9);

C19×#732 #13095294