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C₇×C₁₅₁⋊C₉ #23748877

order	9513
automorphism	?
homology	Abelianization (H₁) = C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₁₅₁⋊C₉
unambiguous semidirect product	C₁₅₁⋊(C₇×C₉)

Splittings

derived, Sylow	C₁₅₁ ⋊ C₇×C₉
Hall	C₇×C₁₅₁ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₇	C₁₅₁⋊C₃
commutator, hypocenter	C₁₅₁	C₇×C₉
Frattini	C₃	C₇×C₁₅₁⋊C₃
Fitting, socle, prime radical	C₃×C₇×C₁₅₁	C₃
cosocle	C₃×C₁₅₁	C₃×C₇
LCS	G ▷ C₁₅₁
UCS	C₁ ◁ C₃×C₇

12 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1113 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₇×C₁₅₁⋊C₉, C₇×D₁₅₁⋊C₉, D₇×C₁₅₁⋊C₉, …
maximal normal subgroup of	C₂×C₇×C₁₅₁⋊C₉, C₇×D₁₅₁⋊C₉, D₇×C₁₅₁⋊C₉, …
maximal quotient of	C₂×C₇×C₁₅₁⋊C₉, C₇×C₂²⋊(C₁₅₁⋊C₉)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9513, 3);