C₂₉×(C₅⋊D₅)⋊C₉ #27189392

order	13050
isoclinism	isoclinic class of (C₅⋊D₅)⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₂₉ · Schur multiplier (H₂) = C₅

Aliases

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

Splittings

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

Subgroups

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

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 1305

A minimal faithful permutation representation — 2 generators on 53 points:

(1,2,4)(3,6,10,7,5,12)(8,13,15,14,11,9)(16,23,22,18,17,24,21,20,19)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53);(1,3,8,14,7)(2,5,11,13,6)(4,9,10,12,15)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#90646⋊C₂, ((C₅⋊D₅)⋊C₉)⋊D₂₉, C₂₉×#1043⋊C₉, …
maximal normal subgroup of	C₂₉×#90646⋊C₂, ((C₅⋊D₅)⋊C₉)⋊D₂₉, C₂₉×#1043⋊C₉, …
maximal quotient of	C₂₉×#1039⋊C₉, C₂×C₂₉×(C₅⋊D₅)⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13050, 24);

C29×(C5⋊D5)⋊C9 #27189392