Finite Group Databasebeta

← Prev (#45691530) Next (#45691532) →

C₉×C₇⋊Dic₁₃₃ #45691531

order	33516
automorphism	?
homology	Abelianization (H₁) = C₄×C₉ · Schur multiplier (H₂) = C₇

Aliases

C₉×C₇⋊Dic₁₃₃

Splittings

derived, Hall	C₇²×C₁₉ ⋊ C₄×C₉
Hall	C₇²×C₉×C₁₉ ⋊ C₄
Hall	C₇²×C₉ ⋊ Dic₁₉
Hall	C₉×C₁₉ ⋊ C₇⋊Dic₇
Sylow	C₇² ⋊ C₉×Dic₁₉
Sylow	C₁₉ ⋊ C₉×C₇⋊Dic₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉	C₇⋊D₁₃₃
commutator, hypocenter	C₇²×C₁₉	C₄×C₉
Frattini	C₂×C₃	C₃×C₇⋊D₁₃₃
Fitting	C₂×C₇²×C₉×C₁₉	C₂
socle, prime radical, cosocle	C₂×C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₂×C₉

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 33516

Conjugacy classes & character table

8406 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 329);