Finite Group Databasebeta

← Prev (#34039743) Next (#34039745) →

C₉×D₇×C₁₅₁ #34039744

order	19026
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₅₁ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₇×C₁₅₁

Splittings

Fitting, Hall	C₇×C₉×C₁₅₁ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₉×C₁₅₁
Hall	C₇×C₁₅₁ ⋊ C₂×C₉
Hall	C₇×C₉ ⋊ C₂×C₁₅₁

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₅₁	D₇
commutator, hypocenter	C₇	C₂×C₉×C₁₅₁
Frattini	C₃	C₃×D₇×C₁₅₁
Fitting	C₇×C₉×C₁₅₁	C₂
socle	C₃×C₇×C₁₅₁	C₂×C₃
prime radical	C₃×D₇×C₁₅₁	C₃
cosocle	C₃×C₇	C₂×C₃×C₁₅₁
LCS	G ▷ C₇
UCS	C₁ ◁ C₉×C₁₅₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9513

Conjugacy classes & character table

6795 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₇×D₁₅₁, D₇×D₉×C₁₅₁, D₇×D₁₃₅₉, …
maximal normal subgroup of	C₉×D₇×D₁₅₁, D₇×D₉×C₁₅₁, D₇×D₁₃₅₉, …
maximal quotient of	C₉×Dic₇×C₁₅₁, C₂×C₉×D₇×C₁₅₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19026, 7);