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D₁₃×C₃⋊(C₇⋊D₇) #21439764

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

Aliases

direct product	D₁₃×C₃⋊(C₇⋊D₇)
unambiguous semidirect product	(C₃×D₁₃)⋊(C₇⋊D₇)
unambiguous semidirect product	(C₇×D₁₃)⋊D₂₁

Splittings

Fitting, socle, derived, Hall	C₃×C₇²×C₁₃ ⋊ C₂²
Hall	C₇²×C₁₃ ⋊ C₂×D₃
Hall	C₃×C₇² ⋊ C₂×D₁₃
Sylow	C₇² ⋊ D₃×D₁₃
Hall	C₃×C₁₃ ⋊ C₂×C₇⋊D₇
Sylow	C₁₃ ⋊ C₂×C₃⋊(C₇⋊D₇)
Sylow	C₃ ⋊ D₁₃×C₇⋊D₇

Subgroups

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

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

600 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₁₃×C₇⋊D₆₃, #10587716⋊D₂₁, #10587717⋊D₂₁, …
maximal normal subgroup of	#10587716⋊D₂₁, #10587717⋊D₂₁, D₁₃×C₃⋊(ΓL(1,𝔽₈)⋊D₇), …
maximal quotient of	D₁₃×C₇⋊D₆₃, C₃×D₁₃×C₃⋊(C₇⋊D₇), D₃₉⋊(C₃⋊(C₇⋊D₇)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7644, 333);