Finite Group Databasebeta

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C₁₃×C₂²⋊#4296 #22580307

order	8892
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₃×C₂²⋊#4296
unambiguous semidirect product	C₂²⋊(C₁₃×#4296)

Splittings

Fitting, socle, Hall	C₂²×C₁₃×C₁₉ ⋊ C₉
derived, Hall	C₂²×C₁₉ ⋊ C₉×C₁₃
Hall	C₁₃×C₁₉ ⋊ C₂²⋊C₉
Hall	C₂²×C₁₃ ⋊ #4296
Sylow	C₁₉ ⋊ C₁₃×C₂²⋊C₉
Sylow	C₂² ⋊ C₁₃×#4296

Subgroups

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

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

260 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 210);