C₃×C₂₉×#3866 #27166155

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

Aliases

direct product

C₃×C₂₉×#3866

Splittings

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

Subgroups

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

(2,6,4,3)(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)(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);(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)

Conjugacy classes & character table

1131 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×#13050613, C₉×C₂₉×#3866, C₃×C₂₉×#3866⋊C₃, …
maximal normal subgroup of	C₂₉×#13050613, C₉×C₂₉×#3866, C₃×C₂₉×#3866⋊C₃, …
maximal quotient of	C₉×C₂₉×#3866, C₃²×C₂₉×#3866, C₃×C₂₉×C₃⋊#3866

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12876, 24);

C3×C29×#3866 #27166155