C₃×#16864283 #27166160

order	12876
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×#16864283

Splittings

Fitting, socle, Hall	C₃×C₂₉×C₃₇ ⋊ C₄
derived, Hall	C₂₉×C₃₇ ⋊ C₃×C₄
Hall	C₃×C₃₇ ⋊ Dic₂₉
Hall	C₃×C₂₉ ⋊ #3866
Sylow	C₃₇ ⋊ C₃×Dic₂₉
Sylow	C₂₉ ⋊ C₃×#3866

Subgroups

	subgroup	G/H
center, hypercenter	C₃	#16864283
commutator, hypocenter	C₂₉×C₃₇	C₃×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₂₉×C₃₇	C₄
prime radical	C₃×C₂₉×D₃₇	C₂
cosocle	C₂₉×D₃₇	C₂×C₃
LCS	G ▷ C₂₉×C₃₇
UCS	C₁ ◁ C₃

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:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	#50311132, C₉×#16864283, C₃×#16864283⋊C₃, …
maximal normal subgroup of	#50311132, C₉×#16864283, C₃×#16864283⋊C₃, …
maximal quotient of	C₉×#16864283, C₃²×#16864283, C₃×C₃⋊#16864283

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12876, 29);

C3×#16864283 #27166160