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D₂₁⋊D₁₂₇ #24922622

order	10668
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	D₂₁⋊D₁₂₇
unambiguous semidirect product	D₃₈₁⋊D₇
unambiguous semidirect product	D₈₈₉⋊D₃

Splittings

Fitting, socle, derived, Hall	C₃×C₇×C₁₂₇ ⋊ C₂²
Hall	C₇×C₁₂₇ ⋊ C₂×D₃
Hall	C₃×C₁₂₇ ⋊ C₂×D₇
Sylow	C₁₂₇ ⋊ D₃×D₇
Hall	C₃×C₇ ⋊ C₂×D₁₂₇
Sylow	C₇ ⋊ D₃×D₁₂₇
Sylow	C₃ ⋊ D₇×D₁₂₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₂₇	C₂²
LCS	G ▷ C₃×C₇×C₁₂₇
UCS	C₁

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^2,3,7,127|d^a=d^6,e^a=e^126,c^b=c^2,d^b=d^6

Conjugacy classes & character table

771 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₆₃⋊D₁₂₇, #19128632⋊D₃, #19128633⋊D₃, …
maximal normal subgroup of	#19128632⋊D₃, #19128633⋊D₃, (C₃⋊AGL(1,𝔽₇))⋊D₁₂₇, …
maximal quotient of	D₆₃⋊D₁₂₇, C₃×D₂₁⋊D₁₂₇, D₃₈₁⋊D₂₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10668, 63);