Finite Group Databasebeta

← Prev (#22580311) Next (#22580313) →

A₄×C₁₉×C₁₃⋊C₃ #22580312

order	8892
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₉ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	A₄×C₁₉×C₁₃⋊C₃
unambiguous semidirect product	(C₂²×C₁₃⋊C₃)⋊(C₃×C₁₉)
unambiguous semidirect product	(A₄×C₁₃)⋊(C₃×C₁₉)
unambiguous semidirect product	(C₂²⋊(C₁₃⋊C₃))⋊(C₃×C₁₉)

Splittings

Fitting, socle, Hall	C₂²×C₁₃×C₁₉ ⋊ C₃²
derived, Hall	C₂²×C₁₃ ⋊ C₃²×C₁₉
Hall	C₁₃×C₁₉ ⋊ C₃×A₄
Hall	C₂²×C₁₉ ⋊ C₃×C₁₃⋊C₃
Sylow	C₁₃ ⋊ C₃×A₄×C₁₉
Sylow	C₂² ⋊ C₃×C₁₉×C₁₃⋊C₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	A₄×C₁₃⋊C₃
commutator, hypocenter	C₂²×C₁₃	C₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₂²×C₁₃×C₁₉	C₃²
LCS	G ▷ C₂²×C₁₃
UCS	C₁ ◁ C₁₉

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

532 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 215);