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D₇×C₃⋊D₃×C₂₉ #20300657

order	7308
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₉ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	D₇×C₃⋊D₃×C₂₉
unambiguous semidirect product	(C₃×D₇)⋊(D₃×C₂₉)

Splittings

Fitting, socle, Hall	C₃²×C₇×C₂₉ ⋊ C₂²
derived, Hall	C₃²×C₇ ⋊ C₂²×C₂₉
Hall	C₃²×C₂₉ ⋊ C₂×D₇
Hall	C₇×C₂₉ ⋊ C₂×C₃⋊D₃
Sylow	C₃² ⋊ C₂×D₇×C₂₉
Sylow	C₇ ⋊ C₂×C₃⋊D₃×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂₉	D₇×C₃⋊D₃
commutator, hypocenter	C₃²×C₇	C₂²×C₂₉
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₂₉	C₂²
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₂₉

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

870 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×D₇×C₃⋊D₃×C₂₉, D₇×C₂₉×C₃⋊D₁₅, C₃⋊D₃×C₂₉×D₃₅, …
maximal normal subgroup of	C₅×D₇×C₃⋊D₃×C₂₉
maximal quotient of	C₅×D₇×C₃⋊D₃×C₂₉, D₇×C₂₉×C₃⋊D₁₅, C₃⋊D₃×C₂₉×D₃₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7308, 132);