Finite Group Databasebeta

← Prev (#36318755) Next (#36318757) →

C₇×C₉×C₁₃⋊D₁₃ #36318756

order	21294
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₉ · Schur multiplier (H₂) = C₁₃

Aliases

C₇×C₉×C₁₃⋊D₁₃

Splittings

Fitting, Hall	C₇×C₉×C₁₃² ⋊ C₂
derived, Sylow	C₁₃² ⋊ C₂×C₇×C₉
Hall	C₉×C₁₃² ⋊ C₂×C₇
Hall	C₇×C₁₃² ⋊ C₂×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₉	C₁₃⋊D₁₃
commutator, hypocenter	C₁₃²	C₂×C₇×C₉
Frattini	C₃	C₃×C₇×C₁₃⋊D₁₃
Fitting	C₇×C₉×C₁₃²	C₂
socle	C₃×C₇×C₁₃²	C₂×C₃
prime radical	C₃×C₇×C₁₃⋊D₁₃	C₃
cosocle	C₃×C₁₃²	C₂×C₃×C₇
LCS	G ▷ C₁₃²
UCS	C₁ ◁ C₇×C₉

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 10647

Conjugacy classes & character table

5418 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21294, 148);