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C₂₉×Dic₁₃⋊C₉ #28330853

order	13572
isoclinism	isoclinic class of D₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₉×Dic₁₃⋊C₉
unambiguous semidirect product	Dic₁₃⋊(C₉×C₂₉)
unambiguous semidirect product	(C₂₉×Dic₁₃)⋊C₉

Splittings

derived, Sylow	C₁₃ ⋊ C₄×C₉×C₂₉
Hall	C₂₉×C₁₃⋊C₉ ⋊ C₄
Hall	C₂₉×Dic₁₃ ⋊ C₉
Hall	C₁₃×C₂₉ ⋊ C₄×C₉
Hall	C₁₃⋊C₉ ⋊ C₄×C₂₉
Hall	Dic₁₃ ⋊ C₉×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₂₉	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₄×C₉×C₂₉
Frattini	C₂×C₃	C₂₉×D₁₃⋊C₃
Fitting, socle, prime radical	C₂×C₃×C₁₃×C₂₉	C₂×C₃
cosocle	C₂×C₃×C₁₃	C₂×C₃×C₂₉
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₂₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 13572

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13572, 11);