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C₇×(C₁₃⋊C₉)⋊D₇ #26039441

order	11466
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×(C₁₃⋊C₉)⋊D₇
unambiguous semidirect product	(C₁₃⋊C₉)⋊(C₇×D₇)

Splittings

derived	C₇×C₁₃ ⋊ C₂×C₇×C₉
Hall	C₇²×C₁₃⋊C₉ ⋊ C₂
Hall	C₇×D₉₁ ⋊ C₉
Hall	C₇²×C₁₃ ⋊ C₂×C₉
Hall	C₁₃⋊C₉ ⋊ C₇×D₇
Sylow	C₇² ⋊ D₁₃⋊C₉
Sylow	C₁₃ ⋊ C₇×C₉×D₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₇	(C₁₃⋊C₃)⋊D₇
commutator, hypocenter	C₇×C₁₃	C₂×C₇×C₉
Frattini	C₃	C₇×(C₁₃⋊C₃)⋊D₇
Fitting, socle	C₃×C₇²×C₁₃	C₂×C₃
prime radical	C₃×C₇×D₉₁	C₃
cosocle	C₃×C₇×C₁₃	C₂×C₃×C₇
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₃×C₇

66 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

609 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₇×D₇×D₁₃⋊C₉, D₇×(C₁₃⋊C₉)⋊D₇, ((C₁₃⋊C₉)⋊D₇)⋊D₇, …
maximal normal subgroup of	C₇×D₇×D₁₃⋊C₉, D₇×(C₁₃⋊C₉)⋊D₇, ((C₁₃⋊C₉)⋊D₇)⋊D₇, …
maximal quotient of	C₇×#15692563, C₂×C₇×(C₁₃⋊C₉)⋊D₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11466, 84);