Finite Group Databasebeta

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C₂×C₁₉×C₂₉⋊C₇ #21440746

order	7714
isoclinism	isoclinic class of C₂₉⋊C₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₁₉×C₂₉⋊C₇
unambiguous semidirect product	(C₂×C₂₉)⋊(C₇×C₁₉)
unambiguous semidirect product	(C₂×C₁₉×C₂₉)⋊C₇

Splittings

Fitting, socle, Hall	C₂×C₁₉×C₂₉ ⋊ C₇
derived, Sylow	C₂₉ ⋊ C₂×C₇×C₁₉
Hall	C₁₉×C₂₉ ⋊ C₂×C₇
Hall	C₂×C₂₉ ⋊ C₇×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉	C₂₉⋊C₇
commutator, hypocenter	C₂₉	C₂×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₁₉×C₂₉	C₇
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₂×C₁₉

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

418 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₄×C₁₉×C₂₉⋊C₇, C₁₉×Dic₂₉⋊C₇, Dic₁₉×C₂₉⋊C₇, …
maximal normal subgroup of	C₄×C₁₉×C₂₉⋊C₇, C₁₉×Dic₂₉⋊C₇, Dic₁₉×C₂₉⋊C₇, …
maximal quotient of	C₄×C₁₉×C₂₉⋊C₇, C₂²×C₁₉×C₂₉⋊C₇, C₂×C₃×C₁₉×C₂₉⋊C₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7714, 2);