C₅₉×D₁₃⋊C₃ #17987181

order	4602
isoclinism	isoclinic class of D₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅₉×D₁₃⋊C₃
unambiguous semidirect product	D₁₃⋊(C₃×C₅₉)
unambiguous semidirect product	(C₁₃⋊C₃)⋊(C₂×C₅₉)
unambiguous semidirect product	(D₁₃×C₅₉)⋊C₃

Splittings

Fitting, socle, Hall	C₁₃×C₅₉ ⋊ C₂×C₃
derived, Sylow	C₁₃ ⋊ C₂×C₃×C₅₉
Hall	C₁₃⋊C₃×C₅₉ ⋊ C₂
Hall	D₁₃×C₅₉ ⋊ C₃
Hall	C₁₃⋊C₃ ⋊ C₂×C₅₉
Hall	D₁₃ ⋊ C₃×C₅₉

Subgroups

	subgroup	G/H
center, hypercenter	C₅₉	D₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₃×C₅₉
Frattini	C₁	G
Fitting, socle	C₁₃×C₅₉	C₂×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₅₉

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 72
transitive degree	μ_t(G) = 767

A minimal faithful permutation representation — 2 generators on 72 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59)(61,65,66,62,63,67)(64,71,70,68,69,72);(60,61,64,63,67,70,69,71,72,66,65,68,62)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₅₉×D₁₃⋊C₃, C₅₉×C₃⋊(D₁₃⋊C₃), C₅×C₅₉×D₁₃⋊C₃, …
maximal normal subgroup of	C₃×C₅₉×D₁₃⋊C₃, C₅×C₅₉×D₁₃⋊C₃, C₇×C₅₉×D₁₃⋊C₃
maximal quotient of	C₅₉×D₁₃⋊C₉, C₃×C₅₉×D₁₃⋊C₃, C₅₉×C₃⋊(D₁₃⋊C₃), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4602, 11);

C59×D13⋊C3 #17987181