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C₇×D₇×C₁₉⋊C₃ #19150282

order	5586
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₇ · Schur multiplier (H₂) = C₁

Aliases

C₇×D₇×C₁₉⋊C₃

Splittings

Fitting, socle, Hall	C₇²×C₁₉ ⋊ C₂×C₃
derived	C₇×C₁₉ ⋊ C₂×C₃×C₇
Hall	C₇²×C₁₉⋊C₃ ⋊ C₂
Hall	C₇×D₇×C₁₉ ⋊ C₃
Sylow	C₇² ⋊ C₂×C₁₉⋊C₃
Sylow	C₁₉ ⋊ C₃×C₇×D₇

Subgroups

	subgroup	G/H
center, hypercenter	C₇	D₇×C₁₉⋊C₃
commutator, hypocenter	C₇×C₁₉	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₇

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

315 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₇×D₇×D₁₉⋊C₃, D₇×(C₁₉⋊C₃)⋊D₇, D₇²×C₁₉⋊C₃, …
maximal normal subgroup of	C₇×D₇×D₁₉⋊C₃, D₇×(C₁₉⋊C₃)⋊D₇, D₇²×C₁₉⋊C₃, …
maximal quotient of	C₇×Dic₇×C₁₉⋊C₃, C₂×C₇×D₇×C₁₉⋊C₃, C₇×D₇×#4294, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5586, 37);