C₂₉×C₁₀₁⋊C₅ #28410753

order	14645
isoclinism	isoclinic class of C₁₀₁⋊C₅
automorphism	?
homology	Abelianization (H₁) = C₅×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₉×C₁₀₁⋊C₅
unambiguous semidirect product	C₁₀₁⋊(C₅×C₂₉)
unambiguous semidirect product	(C₂₉×C₁₀₁)⋊C₅

Splittings

Fitting, socle, Hall	C₂₉×C₁₀₁ ⋊ C₅
derived, Sylow	C₁₀₁ ⋊ C₅×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂₉	C₁₀₁⋊C₅
commutator, cosocle, hypocenter	C₁₀₁	C₅×C₂₉
Frattini	C₁	G
Fitting, socle	C₂₉×C₁₀₁	C₅
LCS	G ▷ C₁₀₁
UCS	C₁ ◁ C₂₉

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 130
transitive degree	μ_t(G) = 2929

A minimal faithful permutation representation — 2 generators on 130 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)(102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130);(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

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

Relationships

maximal subgroup of	C₂×C₂₉×C₁₀₁⋊C₅, C₂₉×D₁₀₁⋊C₅, D₂₉×C₁₀₁⋊C₅, …
maximal normal subgroup of	C₂×C₂₉×C₁₀₁⋊C₅, C₂₉×D₁₀₁⋊C₅, D₂₉×C₁₀₁⋊C₅, …
maximal quotient of	C₂×C₂₉×C₁₀₁⋊C₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14645, 1);

C29×C101⋊C5 #28410753