C₂₉×Dic₁₁₁ #27166138

order	12876
isoclinism	isoclinic class of D₁₁₁
automorphism	?
homology	Abelianization (H₁) = C₄×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₉×Dic₁₁₁
unambiguous semidirect product	C₃⋊(C₂₉×Dic₃₇)

Splittings

derived, Hall	C₃×C₃₇ ⋊ C₄×C₂₉
Hall	C₃×C₂₉×C₃₇ ⋊ C₄
Hall	C₂₉×C₃₇ ⋊ Dic₃
Hall	C₃×C₂₉ ⋊ Dic₃₇
Sylow	C₃₇ ⋊ Dic₃×C₂₉
Sylow	C₃ ⋊ C₂₉×Dic₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₂₉	D₁₁₁
commutator, hypocenter	C₃×C₃₇	C₄×C₂₉
Frattini	C₂	C₂₉×D₁₁₁
Fitting, socle, prime radical	C₂×C₃×C₂₉×C₃₇	C₂
cosocle	C₂×C₃×C₃₇	C₂×C₂₉
LCS	G ▷ C₃×C₃₇
UCS	C₁ ◁ C₂×C₂₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 12876

A minimal faithful permutation representation — 2 generators on 73 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(39,40)(41,42,43,44)(45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(38,39,40)

Conjugacy classes & character table

3306 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×Dic₃₃₃, C₂₉×C₃⋊(Dic₃₇⋊C₃), C₂₉×C₃⋊Dic₁₁₁, …
maximal normal subgroup of	C₂₉×C₃⋊(Dic₃₇⋊C₃), C₃×C₂₉×Dic₁₁₁
maximal quotient of	C₂₉×Dic₃₃₃, C₂₉×C₃⋊Dic₁₁₁, C₃×C₂₉×Dic₁₁₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12876, 7);

C29×Dic111 #27166138