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C₂×C₇×D₇×C₁₃⋊C₃ #21439700

order	7644
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₇ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₇×D₇×C₁₃⋊C₃

Splittings

Fitting, socle	C₂×C₇²×C₁₃ ⋊ C₂×C₃
derived	C₇×C₁₃ ⋊ C₂²×C₃×C₇
Hall	C₂×C₇×C₁₃×D₇ ⋊ C₃
Hall	C₇²×C₁₃⋊C₃ ⋊ C₂²
Hall	C₇²×C₁₃ ⋊ C₂²×C₃
Sylow	C₇² ⋊ C₂²×C₁₃⋊C₃
Sylow	C₁₃ ⋊ C₂×C₃×C₇×D₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₇	D₇×C₁₃⋊C₃
commutator, hypocenter	C₇×C₁₃	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₂×C₇

104 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

490 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₃⋊C₃×#64418, C₂×C₇×C₁₃⋊C₃×AGL(1,𝔽₇), C₂×D₇×ΓL(1,𝔽₈)×C₁₃⋊C₃, …
maximal normal subgroup of	C₂×C₇×C₁₃⋊C₃×AGL(1,𝔽₇), C₂×D₇×ΓL(1,𝔽₈)×C₁₃⋊C₃, C₂×C₁₃⋊C₃×#64423, …
maximal quotient of	C₂×C₇×D₇×C₁₃⋊C₉, D₃×C₇×D₇×C₁₃⋊C₃, C₂×C₃×C₇×D₇×C₁₃⋊C₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7644, 269);