C₂₉×C₅⋊D₄₅ #27189405

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

Aliases

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

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂₉	C₅⋊D₄₅
commutator, cosocle, hypocenter	C₅²×C₉	C₂×C₂₉
Frattini	C₃	C₂₉×C₃⋊(C₅⋊D₅)
Fitting	C₅²×C₉×C₂₉	C₂
socle	C₃×C₅²×C₂₉	D₃
LCS	G ▷ C₅²×C₉
UCS	C₁ ◁ C₂₉

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 48
transitive degree	μ_t(G) = 6525

A minimal faithful permutation representation — 3 generators on 48 points:

(2,4)(3,7)(5,6)(8,9)(11,12)(13,14)(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);(1,9,4,7,6,5,3,2,8)(15,16,18,19,17);(10,11,13,14,12)

Conjugacy classes & character table

3306 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₂₉×C₅⋊D₄₅, D₉×C₂₉×C₅⋊D₅, D₂₆₁⋊(C₅⋊D₅), …
maximal normal subgroup of	D₂₉×C₅⋊D₄₅, D₉×C₂₉×C₅⋊D₅, D₂₆₁⋊(C₅⋊D₅), …
maximal quotient of	C₂₉×C₉⋊#1039, C₂×C₂₉×C₅⋊D₄₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13050, 37);

C29×C5⋊D45 #27189405