C₂₉×#3866⋊C₃ #27166145

order	12876
isoclinism	isoclinic class of #3866⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₉×#3866⋊C₃
unambiguous semidirect product	#3866⋊(C₃×C₂₉)
unambiguous semidirect product	(C₂₉×#3866)⋊C₃

Splittings

Fitting, socle, Hall	C₂₉×C₃₇ ⋊ C₃×C₄
derived, Sylow	C₃₇ ⋊ C₃×C₄×C₂₉
Hall	C₂₉×#3866 ⋊ C₃
Hall	C₂₉×C₃₇⋊C₃ ⋊ C₄
Hall	#3866 ⋊ C₃×C₂₉
Hall	C₃₇⋊C₃ ⋊ C₄×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂₉	#3866⋊C₃
commutator, hypocenter	C₃₇	C₃×C₄×C₂₉
Frattini	C₁	G
Fitting, socle	C₂₉×C₃₇	C₃×C₄
prime radical	C₂₉×D₃₇⋊C₃	C₂
cosocle	D₃₇	C₂×C₃×C₂₉
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₂₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 66
transitive degree	μ_t(G) = 1073

A minimal faithful permutation representation — 2 generators on 66 points:

(2,7,12,8,4,17,5,18,10,3,11,25)(6,27,37,24,14,26,15,30,28,13,29,34)(9,16,36,20,21,32,22,33,35,19,31,23)(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);(1,2,6,16,32,22,8,20,18,34,10,11,24,36,17,14,30,37,21,31,28,27,29,25,35,13,4,12,26,7,19,3,9,23,33,15,5)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×AGL(1,𝔽₃₇), C₃×C₂₉×#3866⋊C₃, C₂₉×C₃⋊(#3866⋊C₃)
maximal normal subgroup of	C₂₉×AGL(1,𝔽₃₇), C₃×C₂₉×#3866⋊C₃
maximal quotient of	C₂₉×#13050613, C₃×C₂₉×#3866⋊C₃, C₂₉×C₃⋊(#3866⋊C₃)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12876, 14);

C29×#3866⋊C3 #27166145