C₃×C₁₉×#737 #17987303

order	4617
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃⁴×C₁₉ · Schur multiplier (H₂) = C₃⁵

Aliases

direct product

C₃×C₁₉×#737

Subgroups

	subgroup	G/H
center	C₃×C₉×C₁₉	C₃²
commutator, Frattini, cosocle	C₃	C₃⁴×C₁₉
socle	C₃²×C₁₉	C₃³
prime radical	C₃×C₁₉×H(3,𝔽₃)	C₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₉×C₁₉ ◁ G

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 1539

A minimal faithful permutation representation — 4 generators on 49 points:

(1,2,3)(31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49);(4,5,8)(6,10,16)(7,11,15)(9,17,14)(12,19,24)(13,20,23)(18,25,22)(21,27,29)(26,30,28);(5,9,11)(8,15,17)(10,18,20)(16,23,25)(19,26,27)(24,29,30);(4,6,12,7,13,21,14,22,28)(5,10,19,11,20,27,9,18,26)(8,16,24,15,23,29,17,25,30)

Conjugacy classes & character table

1881 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#28353182, #28353188, #28353378, …
maximal subgroup of	C₁₉×#10624456, C₁₉×#10624459, C₁₉×#10624510, …
maximal normal subgroup of	C₁₉×#10624456, C₁₉×#10624459, C₁₉×#10624510, …
maximal quotient of	C₃×C₁₉×#6887, C₃×C₉×C₁₉×H(3,𝔽₃), C₃×C₉×C₁₉×3₋¹⁺², …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4617, 64);

C3×C19×#737 #17987303