D₂₉×C₅²⋊C₉ #27189394

order	13050
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₅

Aliases

direct product	D₂₉×C₅²⋊C₉
unambiguous semidirect product	C₂₉⋊(C₂×C₅²⋊C₉)
unambiguous semidirect product	(C₅²×D₂₉)⋊C₉

Splittings

derived, Hall	C₅²×C₂₉ ⋊ C₂×C₉
Hall	C₂₉×C₅²⋊C₉ ⋊ C₂
Hall	C₅²×D₂₉ ⋊ C₉
Sylow	C₂₉ ⋊ C₂×C₅²⋊C₉
Sylow	C₅² ⋊ C₉×D₂₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₂₉×C₅²⋊C₃
commutator, hypocenter	C₅²×C₂₉	C₂×C₉
Fitting, socle, cosocle	C₃×C₅²×C₂₉	C₂×C₃
prime radical	C₃×C₅²×D₂₉	C₃
LCS	G ▷ C₅²×C₂₉
UCS	C₁ ◁ C₃

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	#39907901, D₂₉×#90646, #15668535⋊C₉, …
maximal normal subgroup of	#39907901, D₂₉×#90646, #15668535⋊C₉, …
maximal quotient of	Dic₂₉×C₅²⋊C₉, C₂×D₂₉×C₅²⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13050, 26);

D29×C52⋊C9 #27189394