C₂₉×C₄₃⋊C₃ #16836701

order	3741
isoclinism	isoclinic class of C₄₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₉×C₄₃⋊C₃
unambiguous semidirect product	C₄₃⋊(C₃×C₂₉)
unambiguous semidirect product	(C₂₉×C₄₃)⋊C₃

Splittings

Fitting, socle, Hall	C₂₉×C₄₃ ⋊ C₃
derived, Sylow	C₄₃ ⋊ C₃×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂₉	C₄₃⋊C₃
commutator, cosocle, hypocenter	C₄₃	C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₂₉×C₄₃	C₃
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₂₉

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 72
transitive degree	μ_t(G) = 1247

A minimal faithful permutation representation — 2 generators on 72 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)(33,36,41)(35,39,38)(37,43,51)(40,46,48)(42,49,45)(44,53,62)(47,55,60)(50,58,57)(52,61,54)(56,65,69)(59,66,68)(63,70,64)(67,71,72);(30,31,33,37,44,49,34,38,45,54,64,61,41,48,57,53,63,70,51,60,68,65,43,52,62,69,72,71,55,36,42,50,59,67,66,46,32,35,40,47,56,58,39)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₂₉×C₄₃⋊C₃, C₂₉×C₂²⋊(C₄₃⋊C₃), C₅×C₂₉×C₄₃⋊C₃, …
maximal normal subgroup of	C₃×C₂₉×C₄₃⋊C₃, C₅×C₂₉×C₄₃⋊C₃, C₇×C₂₉×C₄₃⋊C₃, …
maximal quotient of	C₂₉×C₄₃⋊C₉, C₃×C₂₉×C₄₃⋊C₃, C₂₉×C₂²⋊(C₄₃⋊C₃), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3741, 1);

C29×C43⋊C3 #16836701