C₃₁×Dic₃₉ #18012807

order	4836
isoclinism	isoclinic class of D₃₉
automorphism	?
homology	Abelianization (H₁) = C₄×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃₁×Dic₃₉
unambiguous semidirect product	C₃⋊(C₃₁×Dic₁₃)

Splittings

derived, Hall	C₃×C₁₃ ⋊ C₄×C₃₁
Hall	C₃×C₁₃×C₃₁ ⋊ C₄
Hall	C₁₃×C₃₁ ⋊ Dic₃
Hall	C₃×C₃₁ ⋊ Dic₁₃
Sylow	C₁₃ ⋊ Dic₃×C₃₁
Sylow	C₃ ⋊ C₃₁×Dic₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃₁	D₃₉
commutator, hypocenter	C₃×C₁₃	C₄×C₃₁
Frattini	C₂	C₃₁×D₃₉
Fitting, socle, prime radical	C₂×C₃×C₁₃×C₃₁	C₂
cosocle	C₂×C₃×C₁₃	C₂×C₃₁
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₂×C₃₁

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);(32,34,33,35)(37,38)(40,51)(41,50)(42,49)(43,48)(44,47)(45,46)

Conjugacy classes & character table

1302 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃₁×Dic₁₁₇, C₃₁×C₃⋊(Dic₁₃⋊C₃), C₃⋊#18012816, …
maximal normal subgroup of	C₃₁×C₃⋊(Dic₁₃⋊C₃), C₃⋊#18012816, C₃⋊#18012815, …
maximal quotient of	C₃₁×Dic₁₁₇, C₃×C₃₁×Dic₃₉, C₃₁×C₃⋊Dic₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4836, 11);

C31×Dic39 #18012807