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C₅₃×D₇⋊C₉ #20269241

order	6678
isoclinism	isoclinic class of AGL(1,𝔽₇)
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₅₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅₃×D₇⋊C₉
unambiguous semidirect product	D₇⋊(C₉×C₅₃)
unambiguous semidirect product	(C₇⋊C₉)⋊(C₂×C₅₃)
unambiguous semidirect product	(D₇×C₅₃)⋊C₉

Splittings

derived, Sylow	C₇ ⋊ C₂×C₉×C₅₃
Hall	C₅₃×C₇⋊C₉ ⋊ C₂
Hall	D₇×C₅₃ ⋊ C₉
Hall	C₇×C₅₃ ⋊ C₂×C₉
Hall	C₇⋊C₉ ⋊ C₂×C₅₃
Hall	D₇ ⋊ C₉×C₅₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₅₃	AGL(1,𝔽₇)
commutator, hypocenter	C₇	C₂×C₉×C₅₃
Frattini	C₃	AGL(1,𝔽₇)×C₅₃
Fitting, socle	C₃×C₇×C₅₃	C₂×C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₅₃

24 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	D₅₃×D₇⋊C₉, C₂×C₅₃×D₇⋊C₉, C₅×C₅₃×D₇⋊C₉, …
maximal normal subgroup of	D₅₃×D₇⋊C₉, C₂×C₅₃×D₇⋊C₉, C₅×C₅₃×D₇⋊C₉
maximal quotient of	C₅₃×Dic₇⋊C₉, C₂×C₅₃×D₇⋊C₉, C₅×C₅₃×D₇⋊C₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6678, 11);