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C₂×C₂₉×D₇⋊C₉ #20300554

order	7308
isoclinism	isoclinic class of AGL(1,𝔽₇)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₂₉×D₇⋊C₉
unambiguous semidirect product	D₇⋊(C₂×C₉×C₂₉)
unambiguous semidirect product	(C₂×D₇)⋊(C₉×C₂₉)
unambiguous semidirect product	(C₇⋊C₉)⋊(C₂²×C₂₉)
unambiguous semidirect product	(C₂×C₇⋊C₉)⋊(C₂×C₂₉)
unambiguous semidirect product	(C₂×D₇×C₂₉)⋊C₉

Splittings

derived, Sylow	C₇ ⋊ C₂²×C₉×C₂₉
Hall	C₂₉×C₇⋊C₉ ⋊ C₂²
Hall	C₂×D₇×C₂₉ ⋊ C₉
Hall	C₇×C₂₉ ⋊ C₂²×C₉
Hall	C₇⋊C₉ ⋊ C₂²×C₂₉
Hall	C₂×D₇ ⋊ C₉×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₂₉	AGL(1,𝔽₇)
commutator, hypocenter	C₇	C₂²×C₉×C₂₉
Frattini	C₃	C₂×C₂₉×AGL(1,𝔽₇)
Fitting, socle	C₂×C₃×C₇×C₂₉	C₂×C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₂₉

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1218 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₅×C₂₉×D₇⋊C₉, C₂×C₅×C₂₉×D₇⋊C₉, C₂×C₂₉×C₅⋊(D₇⋊C₉)
maximal normal subgroup of	C₂×C₅×C₂₉×D₇⋊C₉
maximal quotient of	D₅×C₂₉×D₇⋊C₉, C₂×C₅×C₂₉×D₇⋊C₉, C₂×C₂₉×C₅⋊(D₇⋊C₉)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7308, 29);