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C₃²×C₁₉×#261 #22580346

order	8892
isoclinism	isoclinic class of #261
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

C₃²×C₁₉×#261

Splittings

Fitting, socle, Hall	C₃²×C₁₃×C₁₉ ⋊ C₄
derived, Sylow	C₁₃ ⋊ C₃²×C₄×C₁₉
Hall	C₁₃×C₁₉ ⋊ C₃²×C₄
Hall	C₃²×C₁₃ ⋊ C₄×C₁₉

Subgroups

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

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1197 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 249);