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D₇×C₁₉×C₁₃⋊C₃ #23780579

order	10374
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

D₇×C₁₉×C₁₃⋊C₃

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	D₇×C₁₃⋊C₃
commutator, cosocle, hypocenter	C₇×C₁₃	C₂×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₁₉

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

665 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₇×C₁₉×D₁₃⋊C₃, D₇×(C₁₃⋊C₃)⋊D₁₉, D₇×D₁₉×C₁₃⋊C₃, …
maximal normal subgroup of	D₇×C₁₉×D₁₃⋊C₃, D₇×(C₁₃⋊C₃)⋊D₁₉, D₇×D₁₉×C₁₃⋊C₃, …
maximal quotient of	C₁₉×Dic₇×C₁₃⋊C₃, C₂×D₇×C₁₉×C₁₃⋊C₃, D₇×C₁₉×C₁₃⋊C₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10374, 70);