Finite Group Databasebeta

← Prev (#32914874) Next (#32914876) →

C₃×D₃×C₇₉⋊C₁₃ #32914875

order	18486
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₃×C₇₉⋊C₁₃
commutator, cosocle, hypocenter	C₃×C₇₉	C₂×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₇₉	C₂×C₁₃
LCS	G ▷ C₃×C₇₉
UCS	C₁ ◁ C₃

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 474

Conjugacy classes & character table

171 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×D₃×D₇₉⋊C₁₃, D₃×C₃⋊(D₇₉⋊C₁₃), D₃²×C₇₉⋊C₁₃, …
maximal normal subgroup of	C₃×D₃×D₇₉⋊C₁₃, D₃×C₃⋊(D₇₉⋊C₁₃), D₃²×C₇₉⋊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, 38);