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C₁₃×C₁₉×#157 #22580375

order	8892
isoclinism	isoclinic class of #157
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₃×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

C₁₃×C₁₉×#157

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃×C₁₉	#157
commutator, hypocenter	C₃²	C₄×C₁₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₁₉	C₄
LCS	G ▷ C₃²
UCS	C₁ ◁ C₁₃×C₁₉

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1482 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8892, 278);