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D₇×D₉⋊C₉ #72230052

order	2268
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

D₇×D₉⋊C₉

Splittings

Fitting, Hall	C₇×C₉⋊C₉ ⋊ C₂²
derived	C₇×C₉ ⋊ C₂²×C₉
Sylow	C₉⋊C₉ ⋊ C₂×D₇
Sylow	C₇ ⋊ C₂×D₉⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₇×AGL(1,ℤ/9)
commutator, hypocenter	C₇×C₉	C₂²×C₉
Frattini	C₃²	C₃×D₃×D₇
Fitting	C₇×C₉⋊C₉	C₂²
socle	C₃²×C₇	C₂×C₃×D₃
prime radical	C₃×D₇×D₉	C₃
cosocle	C₃×C₇×C₉	C₂²×C₃
LCS	G ▷ C₇×C₉
UCS	C₁ ◁ C₃

106 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 106 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 126

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₇×#92265, AGL(1,𝔽₇)×D₉⋊C₉, #72230106, …
maximal normal subgroup of	D₇×#92265, AGL(1,𝔽₇)×D₉⋊C₉, #72230106, …
maximal quotient of	D₇×AGL(1,ℤ/27)

GAP

Past the SmallGroups library coverage — no SmallGroups id.