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C₉×C₁₃×C₇⋊D₇ #26039498

order	11466
isoclinism	isoclinic class of C₇⋊D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₃ · Schur multiplier (H₂) = C₇

Aliases

C₉×C₁₃×C₇⋊D₇

Splittings

Fitting, Hall	C₇²×C₉×C₁₃ ⋊ C₂
derived, Sylow	C₇² ⋊ C₂×C₉×C₁₃
Hall	C₇²×C₁₃ ⋊ C₂×C₉
Hall	C₇²×C₉ ⋊ C₂×C₁₃

Subgroups

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

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3042 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₁₃×C₇⋊D₇, C₉×C₁₃×D₇², C₉×(C₇⋊D₇)⋊D₁₃, …
maximal normal subgroup of	C₉×D₁₃×C₇⋊D₇, C₉×C₁₃×D₇², C₉×(C₇⋊D₇)⋊D₁₃, …
maximal quotient of	C₉×C₁₃×C₇⋊Dic₇, C₂×C₉×C₁₃×C₇⋊D₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11466, 141);