Finite Group Databasebeta

← Prev (#24922392) Next (#24922394) →

C₇×C₁₃×C₁₃⋊C₉ #24922393

order	10647
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₇×C₉×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₁₃×C₁₃⋊C₉
unambiguous semidirect product	C₁₃⋊(C₇×C₉×C₁₃)

Splittings

derived	C₁₃ ⋊ C₇×C₉×C₁₃
Hall	C₇×C₁₃² ⋊ C₉
Sylow	C₁₃² ⋊ C₇×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₇×C₁₃	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₇×C₉×C₁₃
Frattini	C₃	C₇×C₁₃×C₁₃⋊C₃
Fitting, socle, prime radical	C₃×C₇×C₁₃²	C₃
cosocle	C₃×C₁₃	C₃×C₇×C₁₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₇×C₁₃

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1911 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×C₁₃×D₁₃⋊C₉, C₇×(C₁₃⋊C₉)⋊D₁₃, C₇×D₁₃×C₁₃⋊C₉, …
maximal normal subgroup of	C₇×C₁₃×D₁₃⋊C₉, C₇×(C₁₃⋊C₉)⋊D₁₃, C₇×D₁₃×C₁₃⋊C₉, …
maximal quotient of	C₂×C₇×C₁₃×C₁₃⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10647, 15);