Finite Group Databasebeta

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C₉×C₁₉×C₇⋊D₇ #30660626

order	16758
isoclinism	isoclinic class of C₇⋊D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₉ · Schur multiplier (H₂) = C₇

Aliases

C₉×C₁₉×C₇⋊D₇

Splittings

Fitting, Hall	C₇²×C₉×C₁₉ ⋊ C₂
derived, Sylow	C₇² ⋊ C₂×C₉×C₁₉
Hall	C₇²×C₁₉ ⋊ C₂×C₉
Hall	C₇²×C₉ ⋊ C₂×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₉	C₇⋊D₇
commutator, hypocenter	C₇²	C₂×C₉×C₁₉
Frattini	C₃	C₃×C₁₉×C₇⋊D₇
Fitting	C₇²×C₉×C₁₉	C₂
socle	C₃×C₇²×C₁₉	C₂×C₃
prime radical	C₃×C₁₉×C₇⋊D₇	C₃
cosocle	C₃×C₇²	C₂×C₃×C₁₉
LCS	G ▷ C₇²
UCS	C₁ ◁ C₉×C₁₉

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8379

Conjugacy classes & character table

4446 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₁₉×C₇⋊D₇, C₉×D₇²×C₁₉, C₉×(C₇⋊D₇)⋊D₁₉, …
maximal normal subgroup of	C₉×D₁₉×C₇⋊D₇, C₉×D₇²×C₁₉, C₉×(C₇⋊D₇)⋊D₁₉, …
maximal quotient of	C₉×C₁₉×C₇⋊Dic₇, C₂×C₉×C₁₉×C₇⋊D₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16758, 153);