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C₇×D₉×C₄₇ #20238356

order	5922
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₄₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×D₉×C₄₇
unambiguous semidirect product	C₉⋊(C₂×C₇×C₄₇)

Splittings

Fitting, Hall	C₇×C₉×C₄₇ ⋊ C₂
derived, Sylow	C₉ ⋊ C₂×C₇×C₄₇
Hall	C₉×C₄₇ ⋊ C₂×C₇
Hall	C₇×C₉ ⋊ C₂×C₄₇

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₄₇	D₉
commutator, hypocenter	C₉	C₂×C₇×C₄₇
Frattini	C₃	D₃×C₇×C₄₇
Fitting	C₇×C₉×C₄₇	C₂
socle	C₃×C₇×C₄₇	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₇×C₄₇

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1974 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×D₉×D₄₇, D₇×D₉×C₄₇, D₉×D₃₂₉, …
maximal normal subgroup of	C₇×D₉×D₄₇, D₇×D₉×C₄₇, D₉×D₃₂₉, …
maximal quotient of	C₇×Dic₉×C₄₇, C₂×C₇×D₉×C₄₇, C₅×C₇×D₉×C₄₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5922, 9);