C₃×Dic₁₀₃ #11927779

order	1236
isoclinism	isoclinic class of D₁₀₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×Dic₁₀₃

Splittings

derived, Sylow	C₁₀₃ ⋊ C₃×C₄
Hall	C₃×C₁₀₃ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	D₁₀₃
commutator, hypocenter	C₁₀₃	C₃×C₄
Frattini	C₂	C₃×D₁₀₃
Fitting, socle, prime radical	C₂×C₃×C₁₀₃	C₂
cosocle	C₂×C₁₀₃	C₂×C₃
LCS	G ▷ C₁₀₃
UCS	C₁ ◁ C₂×C₃

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 110
transitive degree	μ_t(G) = 1236

A minimal faithful permutation representation — 2 generators on 110 points:

(1,2,3)(4,5)(6,7)(8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110);(4,6,5,7)(9,110)(10,109)(11,108)(12,107)(13,106)(14,105)(15,104)(16,103)(17,102)(18,101)(19,100)(20,99)(21,98)(22,97)(23,96)(24,95)(25,94)(26,93)(27,92)(28,91)(29,90)(30,89)(31,88)(32,87)(33,86)(34,85)(35,84)(36,83)(37,82)(38,81)(39,80)(40,79)(41,78)(42,77)(43,76)(44,75)(45,74)(46,73)(47,72)(48,71)(49,70)(50,69)(51,68)(52,67)(53,66)(54,65)(55,64)(56,63)(57,62)(58,61)(59,60)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	Dic₁₀₃⋊C₉, C₉×Dic₁₀₃, C₃×(C₁₀₃⋊C₃)⋊C₄, …
maximal normal subgroup of	Dic₁₀₃⋊C₉, C₉×Dic₁₀₃, C₃×(C₁₀₃⋊C₃)⋊C₄, …
maximal quotient of	C₉×Dic₁₀₃, C₃²×Dic₁₀₃, C₃×Dic₃₀₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1236, 4);

C3×Dic103 #11927779