D₂₉×D₁₁₁ #27166171

order	12876
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	D₂₉×D₁₁₁
unambiguous semidirect product	(C₃×D₂₉)⋊D₃₇
unambiguous semidirect product	(C₃₇×D₂₉)⋊D₃

Splittings

Fitting, socle, derived, Hall	C₃×C₂₉×C₃₇ ⋊ C₂²
Hall	C₂₉×C₃₇ ⋊ C₂×D₃
Hall	C₃×C₃₇ ⋊ C₂×D₂₉
Hall	C₃×C₂₉ ⋊ C₂×D₃₇
Sylow	C₃₇ ⋊ D₃×D₂₉
Sylow	C₂₉ ⋊ C₂×D₁₁₁
Sylow	C₃ ⋊ D₂₉×D₃₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₂₉×C₃₇	C₂²
LCS	G ▷ C₃×C₂₉×C₃₇
UCS	C₁

40 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)(4,5)(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)(41,42,44,46,48,50,52,54,56,58,60,62,64,66,68,69,67,65,63,61,59,57,55,53,51,49,47,45,43);(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)(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)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₂₉×D₃₃₃, D₂₉×C₃⋊(D₃₇⋊C₃), C₃×D₂₉×D₁₁₁, …
maximal normal subgroup of	D₂₉×C₃⋊(D₃₇⋊C₃), C₃×D₂₉×D₁₁₁
maximal quotient of	D₂₉×D₃₃₃, C₃×D₂₉×D₁₁₁, D₈₇×D₁₁₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12876, 40);

D29×D111 #27166171