C₂₉×C₃⋊#3866 #27166162

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

Aliases

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

Splittings

Fitting, socle, Hall	C₃×C₂₉×C₃₇ ⋊ C₄
derived, Hall	C₃×C₃₇ ⋊ C₄×C₂₉
Hall	C₂₉×C₃₇ ⋊ Dic₃
Hall	C₃×C₂₉ ⋊ #3866
Sylow	C₃₇ ⋊ Dic₃×C₂₉
Sylow	C₃ ⋊ C₂₉×#3866

Subgroups

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

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 3219

A minimal faithful permutation representation — 2 generators on 69 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×C₉⋊#3866, C₂₉×C₃⋊(#3866⋊C₃), C₃×C₂₉×C₃⋊#3866, …
maximal normal subgroup of	C₂₉×C₃⋊(#3866⋊C₃), C₃×C₂₉×C₃⋊#3866
maximal quotient of	C₂₉×C₉⋊#3866, C₃×C₂₉×C₃⋊#3866, C₂₉×C₃⋊(C₃⋊#3866)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12876, 31);

C29×C3⋊#3866 #27166162