C₂₉×Dic₃₉ #17985298

order	4524
isoclinism	isoclinic class of D₃₉
automorphism	?
homology	Abelianization (H₁) = C₄×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₉×Dic₃₉
unambiguous semidirect product	C₃⋊(C₂₉×Dic₁₃)

Splittings

derived, Hall	C₃×C₁₃ ⋊ C₄×C₂₉
Hall	C₃×C₁₃×C₂₉ ⋊ C₄
Hall	C₁₃×C₂₉ ⋊ Dic₃
Hall	C₃×C₂₉ ⋊ Dic₁₃
Sylow	C₁₃ ⋊ Dic₃×C₂₉
Sylow	C₃ ⋊ C₂₉×Dic₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₂₉	D₃₉
commutator, hypocenter	C₃×C₁₃	C₄×C₂₉
Frattini	C₂	C₂₉×D₃₉
Fitting, socle, prime radical	C₂×C₃×C₁₃×C₂₉	C₂
cosocle	C₂×C₃×C₁₃	C₂×C₂₉
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₂×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);(30,32,31,33)(35,36)(38,49)(39,48)(40,47)(41,46)(42,45)(43,44)

Conjugacy classes & character table

1218 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₉×Dic₁₁₇, C₂₉×C₃⋊(Dic₁₃⋊C₃), C₃×C₂₉×Dic₃₉, …
maximal normal subgroup of	C₂₉×C₃⋊(Dic₁₃⋊C₃), C₃×C₂₉×Dic₃₉, C₅×C₂₉×Dic₃₉, …
maximal quotient of	C₂₉×Dic₁₁₇, C₃×C₂₉×Dic₃₉, C₂₉×C₃⋊Dic₃₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4524, 8);

C29×Dic39 #17985298