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C₂²×C₁₃×#4296 #22580303

order	8892
isoclinism	isoclinic class of #4296
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

C₂²×C₁₃×#4296

Splittings

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

Subgroups

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

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 206);