Finite Group Databasebeta

← Prev (#22580267) Next (#22580269) →

C₃×(C₁₉⋊C₃)⋊#261 #22580268

order	8892
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×(C₁₉⋊C₃)⋊#261
unambiguous semidirect product	(C₁₉⋊C₃)⋊(C₃×#261)

Splittings

Fitting, socle	C₃×C₁₃×C₁₉ ⋊ C₃×C₄
derived, Hall	C₁₃×C₁₉ ⋊ C₃²×C₄
Hall	C₃×C₁₃×C₁₉⋊C₃ ⋊ C₄
Hall	C₁₉⋊#261 ⋊ C₃²
Hall	C₃×C₁₉⋊C₃ ⋊ #261
Sylow	C₁₉ ⋊ C₃²×#261
Sylow	C₁₃ ⋊ C₃×(C₁₉⋊C₃)⋊C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₃	(C₁₉⋊C₃)⋊#261
commutator, hypocenter	C₁₃×C₁₉	C₃²×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₁₉	C₃×C₄
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₃

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

135 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 171);