C₃×D₁₃×C₃₁ #14559014

order	2418
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×D₁₃×C₃₁

Splittings

Fitting, socle, Hall	C₃×C₁₃×C₃₁ ⋊ C₂
derived, Sylow	C₁₃ ⋊ C₂×C₃×C₃₁
Hall	C₁₃×C₃₁ ⋊ C₂×C₃
Hall	C₃×C₁₃ ⋊ C₂×C₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₃₁	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₃₁	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₃₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 1209

A minimal faithful permutation representation — 2 generators on 47 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);(5,16)(6,15)(7,14)(8,13)(9,12)(10,11)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₃₁×#261, C₃×C₃₁⋊#261, C₃×D₁₃×D₃₁, …
maximal normal subgroup of	C₃×C₃₁×#261, C₃×C₃₁⋊#261, C₃×D₁₃×D₃₁, …
maximal quotient of	C₃×C₃₁×Dic₁₃, C₂×C₃×D₁₃×C₃₁, C₃×C₅×D₁₃×C₃₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2418, 7);

C3×D13×C31 #14559014