C₂×C₁₃×C₁₀₁⋊C₅ #27190045

order	13130
isoclinism	isoclinic class of C₁₀₁⋊C₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₁₃×C₁₀₁⋊C₅
unambiguous semidirect product	(C₂×C₁₀₁)⋊(C₅×C₁₃)
unambiguous semidirect product	(C₂×C₁₃×C₁₀₁)⋊C₅

Splittings

Fitting, socle, Hall	C₂×C₁₃×C₁₀₁ ⋊ C₅
derived, Sylow	C₁₀₁ ⋊ C₂×C₅×C₁₃
Hall	C₁₃×C₁₀₁ ⋊ C₂×C₅
Hall	C₂×C₁₀₁ ⋊ C₅×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₃	C₁₀₁⋊C₅
commutator, cosocle, hypocenter	C₁₀₁	C₂×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₁₀₁	C₅
LCS	G ▷ C₁₀₁
UCS	C₁ ◁ C₂×C₁₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 116
transitive degree	μ_t(G) = 2626

A minimal faithful permutation representation — 2 generators on 116 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄×C₁₃×C₁₀₁⋊C₅, C₁₃×Dic₁₀₁⋊C₅, Dic₁₃×C₁₀₁⋊C₅, …
maximal normal subgroup of	C₄×C₁₃×C₁₀₁⋊C₅, C₁₃×Dic₁₀₁⋊C₅, Dic₁₃×C₁₀₁⋊C₅, …
maximal quotient of	C₄×C₁₃×C₁₀₁⋊C₅, C₂²×C₁₃×C₁₀₁⋊C₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13130, 2);

C2×C13×C101⋊C5 #27190045