Finite Group Databasebeta

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C₂×#4296⋊D₁₃ #22580257

order	8892
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×#4296⋊D₁₃
unambiguous semidirect product	(C₂×#4296)⋊D₁₃

Splittings

Fitting, socle	C₂×C₁₃×C₁₉ ⋊ C₂×C₉
derived, Hall	C₁₃×C₁₉ ⋊ C₂²×C₉
Hall	C₁₃×#4296 ⋊ C₂²
Hall	C₂×D₂₄₇ ⋊ C₉
Hall	#4296 ⋊ C₂×D₁₃
Sylow	C₁₉ ⋊ C₂×C₉×D₁₃
Sylow	C₁₃ ⋊ C₂×AGL(1,𝔽₁₉)

Subgroups

	subgroup	G/H
center, hypercenter	C₂	#4296⋊D₁₃
commutator, hypocenter	C₁₃×C₁₉	C₂²×C₉
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₁₉	C₂×C₉
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₂

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 160);