Finite Group Databasebeta

← Prev (#24925871) Next (#24925873) →

C₁₃×C₁₉×Dic₁₁ #24925872

order	10868
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×C₁₉×Dic₁₁
unambiguous semidirect product	C₁₁⋊(C₄×C₁₃×C₁₉)

Splittings

derived, Sylow	C₁₁ ⋊ C₄×C₁₃×C₁₉
Hall	C₁₁×C₁₃×C₁₉ ⋊ C₄
Hall	C₁₁×C₁₉ ⋊ C₄×C₁₃
Hall	C₁₁×C₁₃ ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₃×C₁₉	D₁₁
commutator, hypocenter	C₁₁	C₄×C₁₃×C₁₉
Frattini	C₂	C₁₃×C₁₉×D₁₁
Fitting, socle, prime radical	C₂×C₁₁×C₁₃×C₁₉	C₂
cosocle	C₂×C₁₁	C₂×C₁₃×C₁₉
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₁₃×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3458 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₁₃×C₁₉×Dic₁₁, C₁₃×C₁₉×Dic₃₃, C₁₃×Dic₁₁×C₁₉⋊C₃, …
maximal normal subgroup of	C₃×C₁₃×C₁₉×Dic₁₁, C₁₃×Dic₁₁×C₁₉⋊C₃, C₁₉×C₁₃⋊C₃×Dic₁₁, …
maximal quotient of	C₃×C₁₃×C₁₉×Dic₁₁, C₁₃×C₁₉×Dic₃₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10868, 5);