D₃×D₁₀₇₃ #27166172

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

Aliases

direct product	D₃×D₁₀₇₃
unambiguous semidirect product	(D₃×C₂₉)⋊D₃₇
unambiguous semidirect product	(D₃×C₃₇)⋊D₂₉

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 ⋊ D₃×D₃₇
Sylow	C₃ ⋊ C₂×D₁₀₇₃

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

Conjugacy classes & character table

1614 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₉×D₁₀₇₃, D₃×C₂₉⋊(D₃₇⋊C₃), C₃×D₃×D₁₀₇₃, …
maximal normal subgroup of	D₃×C₂₉⋊(D₃₇⋊C₃), C₃×D₃×D₁₀₇₃
maximal quotient of	D₉×D₁₀₇₃, C₃×D₃×D₁₀₇₃, D₃×D₃₂₁₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12876, 41);

D3×D1073 #27166172