Finite Group Databasebeta

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C₃⋊D₃×C₇₉⋊C₁₃ #32914877

order	18486
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃ · Schur multiplier (H₂) = C₃

Aliases

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

Splittings

Fitting, socle, derived, Hall	C₃²×C₇₉ ⋊ C₂×C₁₃
Hall	C₃²×C₇₉⋊C₁₃ ⋊ C₂
Hall	C₃⋊D₃×C₇₉ ⋊ C₁₃
Sylow	C₇₉ ⋊ C₁₃×C₃⋊D₃
Sylow	C₃² ⋊ C₂×C₇₉⋊C₁₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₇₉	C₂×C₁₃
LCS	G ▷ C₃²×C₇₉
UCS	C₁

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 711

Conjugacy classes & character table

114 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	(C₇₉⋊C₁₃)⋊#157, #157×C₇₉⋊C₁₃, (C₃⋊D₃)⋊(D₇₉⋊C₁₃), …
maximal normal subgroup of	(C₇₉⋊C₁₃)⋊#157, #157×C₇₉⋊C₁₃, (C₃⋊D₃)⋊(D₇₉⋊C₁₃), …
maximal quotient of	C₃⋊Dic₃×C₇₉⋊C₁₃, C₂×C₃⋊D₃×C₇₉⋊C₁₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18486, 40);