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C₃×C₇×D₇×C₁₉ #19150336

order	5586
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₇×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₃×C₇×D₇×C₁₉

Splittings

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

Subgroups

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

44 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1995 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₇×D₇×D₁₉, C₃×D₇²×C₁₉, C₃×D₇×D₁₃₃, …
maximal normal subgroup of	C₃×C₇×D₇×D₁₉, C₃×D₇²×C₁₉, C₃×D₇×D₁₃₃, …
maximal quotient of	C₃×C₇×C₁₉×Dic₇, C₂×C₃×C₇×D₇×C₁₉, C₇×C₉×D₇×C₁₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5586, 91);