Finite Group Databasebeta

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D₇×C₁₉×C₃₁ #22551846

order	8246
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₇×C₁₉×C₃₁
unambiguous semidirect product	C₇⋊(C₂×C₁₉×C₃₁)

Splittings

Fitting, socle, Hall	C₇×C₁₉×C₃₁ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₁₉×C₃₁
Hall	C₇×C₃₁ ⋊ C₂×C₁₉
Hall	C₇×C₁₉ ⋊ C₂×C₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉×C₃₁	D₇
commutator, hypocenter	C₇	C₂×C₁₉×C₃₁
Frattini	C₁	G
Fitting, socle	C₇×C₁₉×C₃₁	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₁₉×C₃₁

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2945 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₇×C₁₉×D₃₁, D₇×C₃₁×D₁₉, D₇×D₅₈₉, …
maximal normal subgroup of	D₇×C₁₉×D₃₁, D₇×C₃₁×D₁₉, D₇×D₅₈₉, …
maximal quotient of	C₁₉×Dic₇×C₃₁, C₂×D₇×C₁₉×C₃₁, C₃×D₇×C₁₉×C₃₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8246, 5);