C₃×C₂₉×Dic₁₃ #17985294

order	4524
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×C₂₉×Dic₁₃

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₂₉	D₁₃
commutator, hypocenter	C₁₃	C₃×C₄×C₂₉
Frattini	C₂	C₃×D₁₃×C₂₉
Fitting, socle, prime radical	C₂×C₃×C₁₃×C₂₉	C₂
cosocle	C₂×C₁₃	C₂×C₃×C₂₉
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₂₉

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);(33,35,34,36)(38,49)(39,48)(40,47)(41,46)(42,45)(43,44)

Conjugacy classes & character table

1392 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×C₂₉×Dic₁₃, C₂₉×Dic₁₃⋊C₉, C₃×C₂₉×Dic₁₃⋊C₃, …
maximal normal subgroup of	C₉×C₂₉×Dic₁₃, C₂₉×Dic₁₃⋊C₉, C₃×C₂₉×Dic₁₃⋊C₃, …
maximal quotient of	C₉×C₂₉×Dic₁₃, C₃²×C₂₉×Dic₁₃, C₃×C₂₉×Dic₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4524, 4);

C3×C29×Dic13 #17985294