C₅₉×D₃₇⋊C₃ #27189882

order	13098
isoclinism	isoclinic class of D₃₇⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅₉×D₃₇⋊C₃
unambiguous semidirect product	D₃₇⋊(C₃×C₅₉)
unambiguous semidirect product	(C₃₇⋊C₃)⋊(C₂×C₅₉)
unambiguous semidirect product	(C₅₉×D₃₇)⋊C₃

Splittings

Fitting, socle, Hall	C₃₇×C₅₉ ⋊ C₂×C₃
derived, Sylow	C₃₇ ⋊ C₂×C₃×C₅₉
Hall	C₅₉×C₃₇⋊C₃ ⋊ C₂
Hall	C₅₉×D₃₇ ⋊ C₃
Hall	C₃₇⋊C₃ ⋊ C₂×C₅₉
Hall	D₃₇ ⋊ C₃×C₅₉

Subgroups

	subgroup	G/H
center, hypercenter	C₅₉	D₃₇⋊C₃
commutator, cosocle, hypocenter	C₃₇	C₂×C₃×C₅₉
Frattini	C₁	G
Fitting, socle	C₃₇×C₅₉	C₂×C₃
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₅₉

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 96
transitive degree	μ_t(G) = 2183

A minimal faithful permutation representation — 2 generators on 96 points:

(2,6,7,3,4,8)(5,14,15,9,10,23)(11,26,27,17,18,34)(12,25,21,19,16,13)(20,36,37,29,28,32)(22,24,35,31,30,33)(38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96);(1,2,5,11,18,28,33,34,31,21,7,6,12,20,30,10,16,23,32,37,15,25,14,24,29,19,4,8,13,22,27,35,36,26,17,9,3)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅₉×#3866⋊C₃, C₅₉⋊(#3866⋊C₃), D₅₉×D₃₇⋊C₃, …
maximal normal subgroup of	C₅₉×#3866⋊C₃, C₅₉⋊(#3866⋊C₃), D₅₉×D₃₇⋊C₃, …
maximal quotient of	C₅₉×Dic₃₇⋊C₃, C₂×C₅₉×D₃₇⋊C₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13098, 11);

C59×D37⋊C3 #27189882