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C₁₃×C₁₉×#595 #30680992

order	16796
isoclinism	isoclinic class of #595
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₁₃×C₁₉×#595

Splittings

Fitting, socle, Hall	C₁₃×C₁₇×C₁₉ ⋊ C₄
derived, Sylow	C₁₇ ⋊ C₄×C₁₃×C₁₉
Hall	C₁₇×C₁₉ ⋊ C₄×C₁₃
Hall	C₁₃×C₁₇ ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃×C₁₉	#595
commutator, hypocenter	C₁₇	C₄×C₁₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₃×C₁₇×C₁₉	C₄
prime radical	C₁₃×C₁₉×D₁₇	C₂
cosocle	D₁₇	C₂×C₁₃×C₁₉
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₁₃×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4199

Conjugacy classes & character table

1976 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16796, 10);