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D₇×D₃₉₁ #24926515

order	10948
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	D₇×D₃₉₁
unambiguous semidirect product	(D₇×C₁₇)⋊D₂₃
unambiguous semidirect product	(D₇×C₂₃)⋊D₁₇

Splittings

Fitting, socle, derived, Hall	C₇×C₁₇×C₂₃ ⋊ C₂²
Hall	C₁₇×C₂₃ ⋊ C₂×D₇
Hall	C₇×C₂₃ ⋊ C₂×D₁₇
Hall	C₇×C₁₇ ⋊ C₂×D₂₃
Sylow	C₂₃ ⋊ D₇×D₁₇
Sylow	C₁₇ ⋊ D₇×D₂₃
Sylow	C₇ ⋊ C₂×D₃₉₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₇×C₂₃	C₂²
LCS	G ▷ C₇×C₁₇×C₂₃
UCS	C₁

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

985 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	AGL(1,𝔽₇)×D₃₉₁, C₃×D₇×D₃₉₁, D₂₁×D₃₉₁, …
maximal normal subgroup of	AGL(1,𝔽₇)×D₃₉₁, C₃×D₇×D₃₉₁
maximal quotient of	C₃×D₇×D₃₉₁, D₂₁×D₃₉₁, D₇×D₁₁₇₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10948, 19);