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C₃×C₇×D₇×D₁₃ #21439746

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

Aliases

C₃×C₇×D₇×D₁₃

Splittings

Fitting, socle, Hall	C₃×C₇²×C₁₃ ⋊ C₂²
derived	C₇×C₁₃ ⋊ C₂²×C₃×C₇
Hall	C₇²×C₁₃ ⋊ C₂²×C₃
Hall	C₃×C₇² ⋊ C₂×D₁₃
Sylow	C₇² ⋊ C₂×C₃×D₁₃
Hall	C₃×C₁₃ ⋊ C₂×C₇×D₇
Sylow	C₁₃ ⋊ C₂×C₃×C₇×D₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₇	D₇×D₁₃
commutator, hypocenter	C₇×C₁₃	C₂²×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₃	C₂²
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₃×C₇

104 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

840 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₇×#13109896⋊C₂, C₇×#13109897⋊C₂, C₇×D₁₃×D₇⋊C₉, …
maximal normal subgroup of	C₇×#13109896⋊C₂, C₇×#13109897⋊C₂, C₇×D₁₃×D₇⋊C₉, …
maximal quotient of	C₇×C₉×D₇×D₁₃, C₃²×C₇×D₇×D₁₃, C₃×C₇×D₁₃×D₂₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7644, 315);