Finite Group Databasebeta

← Prev (#32914854) Next (#32914856) →

C₁₃×D₇₉⋊C₉ #32914855

order	18486
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

C₁₃×D₇₉⋊C₉

Splittings

derived, Sylow	C₇₉ ⋊ C₂×C₉×C₁₃
Hall	C₁₃×C₇₉⋊C₉ ⋊ C₂
Hall	C₁₃×D₇₉ ⋊ C₉
Hall	C₁₃×C₇₉ ⋊ C₂×C₉
Hall	C₇₉⋊C₉ ⋊ C₂×C₁₃
Hall	D₇₉ ⋊ C₉×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₃	D₇₉⋊C₃
commutator, hypocenter	C₇₉	C₂×C₉×C₁₃
Frattini	C₃	C₁₃×D₇₉⋊C₃
Fitting, socle	C₃×C₁₃×C₇₉	C₂×C₃
prime radical	C₃×C₁₃×D₇₉	C₃
cosocle	C₃×C₇₉	C₂×C₃×C₁₃
LCS	G ▷ C₇₉
UCS	C₁ ◁ C₃×C₁₃

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9243

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₁₃×D₇₉⋊C₉, C₂×C₁₃×D₇₉⋊C₉
maximal normal subgroup of	D₁₃×D₇₉⋊C₉, C₂×C₁₃×D₇₉⋊C₉
maximal quotient of	C₁₃×Dic₇₉⋊C₉, C₂×C₁₃×D₇₉⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18486, 18);