Finite Group Databasebeta

← Prev (#30680994) Next (#30680996) →

C₁₇×C₁₉×#261 #30680995

order	16796
isoclinism	isoclinic class of #261
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₇×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₁₇×C₁₉×#261

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₁₇×C₁₉	#261
commutator, hypocenter	C₁₃	C₄×C₁₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₁₃×C₁₇×C₁₉	C₄
prime radical	C₁₇×C₁₉×D₁₃	C₂
cosocle	D₁₃	C₂×C₁₇×C₁₉
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₁₇×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4199

Conjugacy classes & character table

2261 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16796, 13);