C₅×C₉×D₅×C₂₉ #27189397

order	13050
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₉×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₉×D₅×C₂₉
unambiguous semidirect product	C₅⋊(C₂×C₅×C₉×C₂₉)

Splittings

Fitting, Hall	C₅²×C₉×C₂₉ ⋊ C₂
derived	C₅ ⋊ C₂×C₅×C₉×C₂₉
Hall	C₅²×C₂₉ ⋊ C₂×C₉
Hall	C₅²×C₉ ⋊ C₂×C₂₉
Sylow	C₅² ⋊ C₂×C₉×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₉×C₂₉	D₅
commutator, hypocenter	C₅	C₂×C₅×C₉×C₂₉
Frattini	C₃	C₃×C₅×D₅×C₂₉
Fitting	C₅²×C₉×C₂₉	C₂
socle	C₃×C₅²×C₂₉	C₂×C₃
prime radical	C₃×C₅×D₅×C₂₉	C₃
cosocle	C₃×C₅	C₂×C₃×C₅×C₂₉
LCS	G ▷ C₅
UCS	C₁ ◁ C₅×C₉×C₂₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 48
transitive degree	μ_t(G) = 2610

A minimal faithful permutation representation — 2 generators on 48 points:

(1,2,3,4,5)(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)(40,41,43,42,44,46,45,47,48);(6,7,9,10,8)

Conjugacy classes & character table

5220 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×C₉×AGL(1,𝔽₅)×C₂₉, C₅×C₉×#10596816, C₅×C₉×D₅×D₂₉, …
maximal normal subgroup of	C₅×C₉×AGL(1,𝔽₅)×C₂₉, C₅×C₉×#10596816, C₅×C₉×D₅×D₂₉, …
maximal quotient of	C₅×C₉×Dic₅×C₂₉, C₂×C₅×C₉×D₅×C₂₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13050, 29);

C5×C9×D5×C29 #27189397