Finite Group Databasebeta

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D₃×C₁₃×C₇₉ #20259704

order	6162
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃×C₇₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×C₁₃×C₇₉
unambiguous semidirect product	C₃⋊(C₂×C₁₃×C₇₉)

Splittings

Fitting, socle, Hall	C₃×C₁₃×C₇₉ ⋊ C₂
derived, Sylow	C₃ ⋊ C₂×C₁₃×C₇₉
Hall	C₃×C₇₉ ⋊ C₂×C₁₃
Hall	C₃×C₁₃ ⋊ C₂×C₇₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃×C₇₉	D₃
commutator, hypocenter	C₃	C₂×C₁₃×C₇₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₇₉	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₁₃×C₇₉

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3081 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×C₁₃×D₇₉, D₃×D₁₃×C₇₉, D₃×D₁₀₂₇, …
maximal normal subgroup of	D₃×C₁₃×D₇₉, D₃×D₁₃×C₇₉, D₃×D₁₀₂₇, …
maximal quotient of	Dic₃×C₁₃×C₇₉, C₂×D₃×C₁₃×C₇₉, C₁₃×D₉×C₇₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6162, 11);