Finite Group Databasebeta

← Prev (#22547873) Next (#22547875) →

C₉×C₁₂₇⋊C₇ #22547874

order	8001
automorphism	?
homology	Abelianization (H₁) = C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₁₂₇⋊C₇
unambiguous semidirect product	(C₉×C₁₂₇)⋊C₇

Splittings

Fitting, Hall	C₉×C₁₂₇ ⋊ C₇
derived, Sylow	C₁₂₇ ⋊ C₇×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	C₁₂₇⋊C₇
commutator, hypocenter	C₁₂₇	C₇×C₉
Frattini	C₃	C₃×C₁₂₇⋊C₇
Fitting	C₉×C₁₂₇	C₇
socle	C₃×C₁₂₇	C₃×C₇
LCS	G ▷ C₁₂₇
UCS	C₁ ◁ C₉

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₉×C₁₂₇⋊C₇, C₉×D₁₂₇⋊C₇, D₉×C₁₂₇⋊C₇, …
maximal normal subgroup of	C₂×C₉×C₁₂₇⋊C₇, C₉×D₁₂₇⋊C₇, D₉×C₁₂₇⋊C₇, …
maximal quotient of	C₂×C₉×C₁₂₇⋊C₇, C₂²⋊C₉×C₁₂₇⋊C₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8001, 3);