C₃×C₁₃×Dic₂₉ #17985293

order	4524
isoclinism	isoclinic class of D₂₉
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×C₁₃×Dic₂₉

Splittings

derived, Sylow	C₂₉ ⋊ C₃×C₄×C₁₃
Hall	C₃×C₁₃×C₂₉ ⋊ C₄
Hall	C₁₃×C₂₉ ⋊ C₃×C₄
Hall	C₃×C₂₉ ⋊ C₄×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃	D₂₉
commutator, hypocenter	C₂₉	C₃×C₄×C₁₃
Frattini	C₂	C₃×C₁₃×D₂₉
Fitting, socle, prime radical	C₂×C₃×C₁₃×C₂₉	C₂
cosocle	C₂×C₂₉	C₂×C₃×C₁₃
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₂×C₃×C₁₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 4524

A minimal faithful permutation representation — 2 generators on 49 points:

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

Conjugacy classes & character table

1248 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×C₁₃×Dic₂₉, Dic₂₉×C₁₃⋊C₉, C₃×C₁₃⋊C₃×Dic₂₉, …
maximal normal subgroup of	C₉×C₁₃×Dic₂₉, Dic₂₉×C₁₃⋊C₉, C₃×C₁₃⋊C₃×Dic₂₉, …
maximal quotient of	C₉×C₁₃×Dic₂₉, C₃²×C₁₃×Dic₂₉, C₃×C₁₃×Dic₈₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4524, 3);

C3×C13×Dic29 #17985293