C₃×C₁₃×Dic₃₁ #18012802

order	4836
isoclinism	isoclinic class of D₃₁
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×C₁₃×Dic₃₁

Splittings

derived, Sylow	C₃₁ ⋊ C₃×C₄×C₁₃
Hall	C₃×C₁₃×C₃₁ ⋊ C₄
Hall	C₁₃×C₃₁ ⋊ C₃×C₄
Hall	C₃×C₃₁ ⋊ C₄×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃	D₃₁
commutator, hypocenter	C₃₁	C₃×C₄×C₁₃
Frattini	C₂	C₃×C₁₃×D₃₁
Fitting, socle, prime radical	C₂×C₃×C₁₃×C₃₁	C₂
cosocle	C₂×C₃₁	C₂×C₃×C₁₃
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₃×C₁₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 4836

A minimal faithful permutation representation — 2 generators on 51 points:

(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16)(17,18)(19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51);(17,19,18,20)(22,51)(23,50)(24,49)(25,48)(26,47)(27,46)(28,45)(29,44)(30,43)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)

Conjugacy classes & character table

1326 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×C₁₃×Dic₃₁, C₁₃×Dic₃₁⋊C₉, C₁₃⋊C₉×Dic₃₁, …
maximal normal subgroup of	C₉×C₁₃×Dic₃₁, C₁₃×Dic₃₁⋊C₉, C₁₃⋊C₉×Dic₃₁, …
maximal quotient of	C₉×C₁₃×Dic₃₁, C₃²×C₁₃×Dic₃₁, C₃×C₁₃×Dic₉₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4836, 6);

C3×C13×Dic31 #18012802