Finite Group Databasebeta

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C₁₃×Dic₆₅⋊C₉ #44477586

order	30420
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×Dic₆₅⋊C₉
unambiguous semidirect product	Dic₆₅⋊(C₉×C₁₃)

Splittings

derived	C₅×C₁₃ ⋊ C₄×C₉×C₁₃
Hall	C₅×C₁₃×C₁₃⋊C₉ ⋊ C₄
Hall	C₁₃×Dic₆₅ ⋊ C₉
Hall	C₁₃×C₁₃⋊C₉ ⋊ Dic₅
Hall	C₅×C₁₃² ⋊ C₄×C₉
Sylow	C₁₃² ⋊ C₉×Dic₅
Sylow	C₅ ⋊ C₁₃×Dic₁₃⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃	C₅⋊(D₁₃⋊C₃)
commutator, hypocenter	C₅×C₁₃	C₄×C₉×C₁₃
Frattini	C₂×C₃	C₁₃×C₅⋊(D₁₃⋊C₃)
Fitting, socle, prime radical	C₂×C₃×C₅×C₁₃²	C₂×C₃
cosocle	C₂×C₃×C₅×C₁₃	C₂×C₃×C₁₃
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₂×C₃×C₁₃

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2340

Conjugacy classes & character table

1716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30420, 175);