C₃×D₇×C₁₀₃ #16864489

order	4326
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₀₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×D₇×C₁₀₃

Splittings

Fitting, socle, Hall	C₃×C₇×C₁₀₃ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₃×C₁₀₃
Hall	C₇×C₁₀₃ ⋊ C₂×C₃
Hall	C₃×C₇ ⋊ C₂×C₁₀₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₀₃	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₃×C₁₀₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₀₃	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₁₀₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 113
transitive degree	μ_t(G) = 2163

A minimal faithful permutation representation — 2 generators on 113 points:

(1,2,3)(4,5,6,7,8,9,10)(11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113);(5,10)(6,9)(7,8)

Conjugacy classes & character table

1545 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₇×C₁₀₃, D₇×C₁₀₃⋊C₉, C₁₀₃×D₇⋊C₉, …
maximal normal subgroup of	C₉×D₇×C₁₀₃, D₇×C₁₀₃⋊C₉, C₁₀₃×D₇⋊C₉, …
maximal quotient of	C₉×D₇×C₁₀₃, C₃×D₂₁×C₁₀₃, C₃²×D₇×C₁₀₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4326, 7);

C3×D7×C103 #16864489