C₃×Dic₁₀₇₃ #27166136

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

Aliases

direct product

C₃×Dic₁₀₇₃

Splittings

derived, Hall	C₂₉×C₃₇ ⋊ C₃×C₄
Hall	C₃×C₂₉×C₃₇ ⋊ C₄
Hall	C₃×C₃₇ ⋊ Dic₂₉
Hall	C₃×C₂₉ ⋊ Dic₃₇
Sylow	C₃₇ ⋊ C₃×Dic₂₉
Sylow	C₂₉ ⋊ C₃×Dic₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	D₁₀₇₃
commutator, hypocenter	C₂₉×C₃₇	C₃×C₄
Frattini	C₂	C₃×D₁₀₇₃
Fitting, socle, prime radical	C₂×C₃×C₂₉×C₃₇	C₂
cosocle	C₂×C₂₉×C₃₇	C₂×C₃
LCS	G ▷ C₂₉×C₃₇
UCS	C₁ ◁ C₂×C₃

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)(67,70,69,68)(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)(38,39,41,43,45,47,49,51,53,55,57,59,61,63,65,66,64,62,60,58,56,54,52,50,48,46,44,42,40)

Conjugacy classes & character table

3228 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×Dic₁₀₇₃, #50311125, C₃×Dic₁₀₇₃⋊C₃, …
maximal normal subgroup of	C₉×Dic₁₀₇₃, #50311125, C₃×Dic₁₀₇₃⋊C₃, …
maximal quotient of	C₉×Dic₁₀₇₃, C₃×Dic₃₂₁₉, C₃²×Dic₁₀₇₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12876, 5);

C3×Dic1073 #27166136