C₁₀₁×C₄₁⋊C₅ #35208462

order	20705
isoclinism	isoclinic class of C₄₁⋊C₅
automorphism	?
homology	Abelianization (H₁) = C₅×C₁₀₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₀₁×C₄₁⋊C₅
unambiguous semidirect product	C₄₁⋊(C₅×C₁₀₁)

Splittings

Fitting, socle, Hall	C₄₁×C₁₀₁ ⋊ C₅
derived, Sylow	C₄₁ ⋊ C₅×C₁₀₁

Subgroups

	subgroup	G/H
center, hypercenter	C₁₀₁	C₄₁⋊C₅
commutator, cosocle, hypocenter	C₄₁	C₅×C₁₀₁
Frattini	C₁	G
Fitting, socle	C₄₁×C₁₀₁	C₅
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₁₀₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 142
transitive degree	μ_t(G) = 4141

A minimal faithful permutation representation — 2 generators on 142 points:

(2,3,5,9,17)(4,7,13,24,35)(6,11,20,12,22)(8,15,23,34,21)(10,19,30,18,29)(14,25,36,40,33)(16,28,27,38,41)(26,37,31,39,32)(42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142);(1,2,4,8,16,25,29,34,40,36,3,6,12,23,30,37,9,18,5,10,7,14,26,38,39,41,19,31,11,21,15,27,24,35,20,32,13,17,22,33,28)

Conjugacy classes & character table

1313 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20705, 1);

C101×C41⋊C5 #35208462