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C₂₉×(C₃⋊D₃)⋊D₇ #20300668

order	7308
isoclinism	isoclinic class of (C₃⋊D₃)⋊D₇
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂₉×(C₃⋊D₃)⋊D₇
unambiguous semidirect product	(C₃⋊D₃)⋊(D₇×C₂₉)
unambiguous semidirect product	D₂₁⋊(D₃×C₂₉)

Splittings

Fitting, socle, Hall	C₃²×C₇×C₂₉ ⋊ C₂²
derived, Hall	C₃²×C₇ ⋊ C₂²×C₂₉
Hall	C₃²×C₂₉ ⋊ C₂×D₇
Hall	C₇×C₂₉ ⋊ D₃²
Sylow	C₃² ⋊ C₂×D₇×C₂₉
Sylow	C₇ ⋊ D₃²×C₂₉

Subgroups

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

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

783 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×C₂₉×(C₃⋊D₃)⋊D₇, C₂₉×D₂₁⋊D₁₅, C₂₉×(C₃⋊D₃)⋊D₃₅
maximal normal subgroup of	C₅×C₂₉×(C₃⋊D₃)⋊D₇
maximal quotient of	C₅×C₂₉×(C₃⋊D₃)⋊D₇, C₂₉×D₂₁⋊D₁₅, C₂₉×(C₃⋊D₃)⋊D₃₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7308, 143);