C₃₁×D₃₉ #14559018

order	2418
isoclinism	isoclinic class of D₃₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃₁×D₃₉
unambiguous semidirect product	C₃⋊(D₁₃×C₃₁)
unambiguous semidirect product	C₁₃⋊(D₃×C₃₁)

Splittings

Fitting, socle, Hall	C₃×C₁₃×C₃₁ ⋊ C₂
derived, Hall	C₃×C₁₃ ⋊ C₂×C₃₁
Hall	C₁₃×C₃₁ ⋊ D₃
Hall	C₃×C₃₁ ⋊ D₁₃
Sylow	C₁₃ ⋊ D₃×C₃₁
Sylow	C₃ ⋊ D₁₃×C₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃₁	D₃₉
commutator, cosocle, hypocenter	C₃×C₁₃	C₂×C₃₁
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₃₁	C₂
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ 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);(33,34)(36,47)(37,46)(38,45)(39,44)(40,43)(41,42)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₃₁×D₃₉, D₃×D₁₃×C₃₁, D₃₉⋊D₃₁, …
maximal normal subgroup of	D₃₁×D₃₉, D₃×D₁₃×C₃₁, D₃₉⋊D₃₁, …
maximal quotient of	C₃₁×Dic₃₉, C₂×C₃₁×D₃₉, C₅×C₃₁×D₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2418, 11);

C31×D39 #14559018