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C₂×D₂₉×C₁₃⋊C₉ #28330865

order	13572
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×D₂₉×C₁₃⋊C₉
unambiguous semidirect product	C₂₉⋊(C₂²×C₁₃⋊C₉)
unambiguous semidirect product	(C₂×C₂₉)⋊(C₂×C₁₃⋊C₉)
unambiguous semidirect product	(C₂×C₁₃×D₂₉)⋊C₉

Splittings

derived, Hall	C₁₃×C₂₉ ⋊ C₂²×C₉
Hall	C₂₉×C₁₃⋊C₉ ⋊ C₂²
Hall	C₂×C₁₃×D₂₉ ⋊ C₉
Sylow	C₂₉ ⋊ C₂²×C₁₃⋊C₉
Sylow	C₁₃ ⋊ C₂×C₉×D₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	C₁₃⋊C₃×D₂₉
commutator, hypocenter	C₁₃×C₂₉	C₂²×C₉
Frattini	C₃	C₂×C₁₃⋊C₃×D₂₉
Fitting, socle	C₂×C₃×C₁₃×C₂₉	C₂×C₃
prime radical	C₂×C₃×C₁₃×D₂₉	C₃
cosocle	C₃×C₁₃×C₂₉	C₂²×C₃
LCS	G ▷ C₁₃×C₂₉
UCS	C₁ ◁ C₂×C₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 6786

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13572, 23);