C₅×C₂₉×D₄₅ #27189403

order	13050
isoclinism	isoclinic class of D₄₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₂₉×D₄₅
unambiguous semidirect product	C₅⋊(C₅×D₉×C₂₉)
unambiguous semidirect product	C₉⋊(C₅×D₅×C₂₉)

Splittings

Fitting, Hall	C₅²×C₉×C₂₉ ⋊ C₂
derived	C₅×C₉ ⋊ C₂×C₅×C₂₉
Hall	C₅²×C₂₉ ⋊ D₉
Hall	C₉×C₂₉ ⋊ C₅×D₅
Hall	C₅²×C₉ ⋊ C₂×C₂₉
Sylow	C₅² ⋊ D₉×C₂₉
Sylow	C₉ ⋊ C₅×D₅×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₂₉	D₄₅
commutator, cosocle, hypocenter	C₅×C₉	C₂×C₅×C₂₉
Frattini	C₃	C₅×C₂₉×D₁₅
Fitting	C₅²×C₉×C₂₉	C₂
socle	C₃×C₅²×C₂₉	D₃
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₅×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)(12,14)(13,17)(15,16)(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);(6,7,9,10,8)(11,19,14,17,16,15,13,12,18)

Conjugacy classes & character table

3480 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×D₂₉×D₄₅, C₅×D₅×D₉×C₂₉, C₅×D₄₅⋊D₂₉, …
maximal normal subgroup of	C₅×D₂₉×D₄₅, C₅×D₅×D₉×C₂₉, C₅×D₄₅⋊D₂₉, …
maximal quotient of	C₅×C₂₉×Dic₄₅, C₂×C₅×C₂₉×D₄₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13050, 35);

C5×C29×D45 #27189403