C₂×C₁₃⋊(D₁₀₁⋊C₅) #39910967

order	26260
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₁₃⋊(D₁₀₁⋊C₅)
unambiguous semidirect product	(C₂×C₁₃)⋊(D₁₀₁⋊C₅)
unambiguous semidirect product	(C₂×C₁₀₁⋊C₅)⋊D₁₃
unambiguous semidirect product	(C₂×D₁₃₁₃)⋊C₅

Splittings

Fitting, socle	C₂×C₁₃×C₁₀₁ ⋊ C₂×C₅
derived, Hall	C₁₃×C₁₀₁ ⋊ C₂²×C₅
Hall	C₁₃×C₁₀₁⋊C₅ ⋊ C₂²
Hall	C₂×D₁₃₁₃ ⋊ C₅
Hall	C₁₀₁⋊C₅ ⋊ C₂×D₁₃
Sylow	C₁₀₁ ⋊ C₂×C₅×D₁₃
Sylow	C₁₃ ⋊ C₂×D₁₀₁⋊C₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂	C₁₃⋊(D₁₀₁⋊C₅)
commutator, cosocle, hypocenter	C₁₃×C₁₀₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₁₀₁	C₂×C₅
LCS	G ▷ C₁₃×C₁₀₁
UCS	C₁ ◁ C₂

40 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:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26260, 22);

C2×C13⋊(D101⋊C5) #39910967