Dic₃×C₁₃×C₂₉ #17985296

order	4524
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₃×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₃×C₁₃×C₂₉
unambiguous semidirect product	C₃⋊(C₄×C₁₃×C₂₉)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₃×C₂₉	D₃
commutator, hypocenter	C₃	C₄×C₁₃×C₂₉
Frattini	C₂	D₃×C₁₃×C₂₉
Fitting, socle, prime radical	C₂×C₃×C₁₃×C₂₉	C₂
cosocle	C₂×C₃	C₂×C₁₃×C₂₉
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₁₃×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);(1,3,2,4)(6,7)

Conjugacy classes & character table

2262 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₃×C₂₉×Dic₉, Dic₃×C₂₉×C₁₃⋊C₃, C₃×Dic₃×C₁₃×C₂₉, …
maximal normal subgroup of	Dic₃×C₂₉×C₁₃⋊C₃, C₃×Dic₃×C₁₃×C₂₉, C₅×Dic₃×C₁₃×C₂₉, …
maximal quotient of	C₁₃×C₂₉×Dic₉, C₃×Dic₃×C₁₃×C₂₉, C₁₃×C₂₉×C₃⋊Dic₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4524, 6);

Dic3×C13×C29 #17985296