Finite Group Databasebeta

← Prev (#30658198) Next (#30658200) →

C₂×C₇⋊C₉×C₁₃₁ #30658199

order	16506
isoclinism	isoclinic class of ΓL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₇⋊C₉×C₁₃₁
unambiguous semidirect product	(C₂×C₇)⋊(C₉×C₁₃₁)
unambiguous semidirect product	(C₂×C₇×C₁₃₁)⋊C₉

Splittings

derived, Sylow	C₇ ⋊ C₂×C₉×C₁₃₁
Hall	C₂×C₇×C₁₃₁ ⋊ C₉
Hall	C₇×C₁₃₁ ⋊ C₂×C₉
Hall	C₂×C₇ ⋊ C₉×C₁₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃₁	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₂×C₉×C₁₃₁
Frattini	C₃	C₂×ΓL(1,𝔽₈)×C₁₃₁
Fitting, socle, prime radical	C₂×C₃×C₇×C₁₃₁	C₃
cosocle	C₃×C₇	C₂×C₃×C₁₃₁
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₁₃₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 16506

Conjugacy classes & character table

3930 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₇⋊C₉×C₁₃₁, C₇⋊C₉×Dic₁₃₁, C₁₃₁×Dic₇⋊C₉, …
maximal normal subgroup of	C₄×C₇⋊C₉×C₁₃₁, C₇⋊C₉×Dic₁₃₁, C₁₃₁×Dic₇⋊C₉, …
maximal quotient of	C₄×C₇⋊C₉×C₁₃₁, C₂²×C₇⋊C₉×C₁₃₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16506, 2);