C₁₀₃×D₆₅ #27211484

order	13390
isoclinism	isoclinic class of D₆₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₀₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₀₃×D₆₅
unambiguous semidirect product	C₅⋊(D₁₃×C₁₀₃)
unambiguous semidirect product	C₁₃⋊(D₅×C₁₀₃)

Splittings

Fitting, socle, Hall	C₅×C₁₃×C₁₀₃ ⋊ C₂
derived, Hall	C₅×C₁₃ ⋊ C₂×C₁₀₃
Hall	C₁₃×C₁₀₃ ⋊ D₅
Hall	C₅×C₁₀₃ ⋊ D₁₃
Sylow	C₁₃ ⋊ D₅×C₁₀₃
Sylow	C₅ ⋊ D₁₃×C₁₀₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₀₃	D₆₅
commutator, cosocle, hypocenter	C₅×C₁₃	C₂×C₁₀₃
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₁₀₃	C₂
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₁₀₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 121
transitive degree	μ_t(G) = 6695

A minimal faithful permutation representation — 2 generators on 121 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(15,16)(17,18)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121);(1,2,4,6,8,10,12,13,11,9,7,5,3)(14,15,17,18,16)

Conjugacy classes & character table

3502 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₃×#63122, C₁₀₃⋊#63122, C₁₀₃×#63121, …
maximal normal subgroup of	C₁₀₃×#63122, C₁₀₃⋊#63122, C₁₀₃×#63121, …
maximal quotient of	C₁₀₃×Dic₆₅, C₂×C₁₀₃×D₆₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13390, 7);

C103×D65 #27211484