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C₇×D₉×C₅₉ #21418268

order	7434
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₅₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×D₉×C₅₉
unambiguous semidirect product	C₉⋊(C₂×C₇×C₅₉)

Splittings

Fitting, Hall	C₇×C₉×C₅₉ ⋊ C₂
derived, Sylow	C₉ ⋊ C₂×C₇×C₅₉
Hall	C₉×C₅₉ ⋊ C₂×C₇
Hall	C₇×C₉ ⋊ C₂×C₅₉

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₅₉	D₉
commutator, hypocenter	C₉	C₂×C₇×C₅₉
Frattini	C₃	D₃×C₇×C₅₉
Fitting	C₇×C₉×C₅₉	C₂
socle	C₃×C₇×C₅₉	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₇×C₅₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2478 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×D₉×D₅₉, D₇×D₉×C₅₉, D₉×D₄₁₃, …
maximal normal subgroup of	C₇×D₉×D₅₉, D₇×D₉×C₅₉, D₉×D₄₁₃, …
maximal quotient of	C₇×Dic₉×C₅₉, C₂×C₇×D₉×C₅₉, C₅×C₇×D₉×C₅₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7434, 6);