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C₂×D₇×C₆₇⋊C₃ #19150613

order	5628
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

C₂×D₇×C₆₇⋊C₃

Splittings

Fitting, socle	C₂×C₇×C₆₇ ⋊ C₂×C₃
derived, Hall	C₇×C₆₇ ⋊ C₂²×C₃
Hall	C₂×D₇×C₆₇ ⋊ C₃
Hall	C₇×C₆₇⋊C₃ ⋊ C₂²
Sylow	C₆₇ ⋊ C₂×C₃×D₇
Sylow	C₇ ⋊ C₂²×C₆₇⋊C₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₇×C₆₇⋊C₃
commutator, hypocenter	C₇×C₆₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₆₇	C₂×C₃
LCS	G ▷ C₇×C₆₇
UCS	C₁ ◁ C₂

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

250 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×AGL(1,𝔽₇)×C₆₇⋊C₃, D₃×D₇×C₆₇⋊C₃, C₂×C₃×D₇×C₆₇⋊C₃, …
maximal normal subgroup of	C₂×AGL(1,𝔽₇)×C₆₇⋊C₃, C₂×C₃×D₇×C₆₇⋊C₃, C₂×C₅×D₇×C₆₇⋊C₃
maximal quotient of	C₂×D₇×C₆₇⋊C₉, D₃×D₇×C₆₇⋊C₃, C₂×C₃×D₇×C₆₇⋊C₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5628, 41);