C₅×D₁₃×C₂₉ #16836813

order	3770
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₁₃×C₂₉
unambiguous semidirect product	C₁₃⋊(C₂×C₅×C₂₉)

Splittings

Fitting, socle, Hall	C₅×C₁₃×C₂₉ ⋊ C₂
derived, Sylow	C₁₃ ⋊ C₂×C₅×C₂₉
Hall	C₁₃×C₂₉ ⋊ C₂×C₅
Hall	C₅×C₁₃ ⋊ C₂×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₅×C₂₉	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₅×C₂₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₂₉	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₅×C₂₉

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 1885

A minimal faithful permutation representation — 2 generators on 47 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);(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)

Conjugacy classes & character table

1160 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₅×D₁₃×C₂₉, C₅×C₂₉×D₃₉, C₅×C₂₉×D₁₃⋊C₃, …
maximal normal subgroup of	C₃×C₅×D₁₃×C₂₉, C₅×C₂₉×D₁₃⋊C₃, C₂₅×D₁₃×C₂₉, …
maximal quotient of	C₃×C₅×D₁₃×C₂₉, C₅×C₂₉×D₃₉, C₂₅×D₁₃×C₂₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3770, 3);

C5×D13×C29 #16836813