C₂₉×C₁₃⋊C₉ #16811706

order	3393
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₉×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₉×C₁₃⋊C₉
unambiguous semidirect product	C₁₃⋊(C₉×C₂₉)
unambiguous semidirect product	(C₁₃×C₂₉)⋊C₉

Splittings

derived, Sylow	C₁₃ ⋊ C₉×C₂₉
Hall	C₁₃×C₂₉ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₂₉	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₉×C₂₉
Frattini	C₃	C₂₉×C₁₃⋊C₃
Fitting, socle, prime radical	C₃×C₁₃×C₂₉	C₃
cosocle	C₃×C₁₃	C₃×C₂₉
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₂₉

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 3393

A minimal faithful permutation representation — 2 generators on 51 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)(31,32,34)(33,36,39)(35,38,37)(40,42,41)(43,44,46,45,47,49,48,50,51);(30,31,33,32,35,39,36,40,42,34,37,41,38)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×C₂²⋊(C₁₃⋊C₉), C₅×C₂₉×C₁₃⋊C₉, C₇×C₂₉×C₁₃⋊C₉, …
maximal normal subgroup of	C₅×C₂₉×C₁₃⋊C₉, C₇×C₂₉×C₁₃⋊C₉, C₁₃⋊C₉×C₂₉⋊C₇, …
maximal quotient of	C₂₉×C₂²⋊(C₁₃⋊C₉), C₅×C₂₉×C₁₃⋊C₉, C₇×C₂₉×C₁₃⋊C₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3393, 2);

C29×C13⋊C9 #16811706