C₂₉×D₆₁ #16812985

order	3538
isoclinism	isoclinic class of D₆₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₉×D₆₁
unambiguous semidirect product	C₆₁⋊(C₂×C₂₉)

Splittings

Fitting, socle, Hall	C₂₉×C₆₁ ⋊ C₂
derived, Sylow	C₆₁ ⋊ C₂×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂₉	D₆₁
commutator, cosocle, hypocenter	C₆₁	C₂×C₂₉
Frattini	C₁	G
Fitting, socle	C₂₉×C₆₁	C₂
LCS	G ▷ C₆₁
UCS	C₁ ◁ C₂₉

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 90
transitive degree	μ_t(G) = 1769

A minimal faithful permutation representation — 2 generators on 90 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)(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);(31,90)(32,89)(33,88)(34,87)(35,86)(36,85)(37,84)(38,83)(39,82)(40,81)(41,80)(42,79)(43,78)(44,77)(45,76)(46,75)(47,74)(48,73)(49,72)(50,71)(51,70)(52,69)(53,68)(54,67)(55,66)(56,65)(57,64)(58,63)(59,62)(60,61)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅×C₂₉×D₆₁, C₂₉×D₃₀₅, C₂₉×D₆₁⋊C₅, …
maximal normal subgroup of	C₅×C₂₉×D₆₁, C₂₉×D₆₁⋊C₅, C₇×C₂₉×D₆₁, …
maximal quotient of	C₅×C₂₉×D₆₁, C₂₉×D₃₀₅, C₇×C₂₉×D₆₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3538, 2);

C29×D61 #16812985