Finite Group Databasebeta

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C₁₇×C₁₉×Dic₁₃ #30680987

order	16796
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₇×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₁₇×C₁₉×Dic₁₃

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₇×C₁₉	D₁₃
commutator, hypocenter	C₁₃	C₄×C₁₇×C₁₉
Frattini	C₂	C₁₇×C₁₉×D₁₃
Fitting, socle, prime radical	C₂×C₁₃×C₁₇×C₁₉	C₂
cosocle	C₂×C₁₃	C₂×C₁₇×C₁₉
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₇×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 16796

Conjugacy classes & character table

5168 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16796, 5);