C₃×C₂₉⋊#3874 #27189409

order	13050
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₂₉⋊#3874
unambiguous semidirect product	C₂₉⋊(C₃×#3874)

Splittings

Fitting, socle	C₃×C₅²×C₂₉ ⋊ D₃
derived	C₂₉×C₅²⋊C₃ ⋊ C₂×C₃
Hall	C₃×C₂₉×C₅²⋊C₃ ⋊ C₂
Hall	C₅²×C₂₉ ⋊ C₃×D₃
Hall	C₃×C₅²⋊C₃ ⋊ D₂₉
Sylow	C₂₉ ⋊ C₃×#3874
Sylow	C₅² ⋊ C₃×D₈₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃	C₂₉⋊#3874
commutator, cosocle, hypocenter	C₂₉×C₅²⋊C₃	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₂₉	D₃
LCS	G ▷ C₂₉×C₅²⋊C₃
UCS	C₁ ◁ C₃

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 1305

A minimal faithful permutation representation — 2 generators on 47 points:

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

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

Relationships

maximal subgroup of	C₃×D₂₉×#3874, C₃×#3874⋊D₂₉, C₃×((C₅⋊D₅)⋊C₃)⋊D₂₉, …
maximal normal subgroup of	C₃×D₂₉×#3874, C₃×#3874⋊D₂₉, C₃×((C₅⋊D₅)⋊C₃)⋊D₂₉, …
maximal quotient of	C₃×#22576397, C₂×C₃×C₂₉⋊#3874

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13050, 41);

C3×C29⋊#3874 #27189409