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D₃₅×#4296 #26046148

order	11970
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃₅×#4296
unambiguous semidirect product	C₅⋊(D₇×#4296)

Splittings

Fitting, socle, derived, Hall	C₅×C₇×C₁₉ ⋊ C₂×C₉
Hall	C₅×C₇×#4296 ⋊ C₂
Hall	C₁₉×D₃₅ ⋊ C₉
Hall	C₇×#4296 ⋊ D₅
Hall	C₅×#4296 ⋊ D₇
Hall	C₇×C₁₉ ⋊ C₉×D₅
Hall	C₅×C₁₉ ⋊ C₉×D₇
Hall	C₅×C₇ ⋊ C₂×#4296
Sylow	C₁₉ ⋊ C₉×D₃₅
Sylow	C₇ ⋊ D₅×#4296
Sylow	C₅ ⋊ D₇×#4296

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₇×C₁₉	C₂×C₉
prime radical	C₁₉⋊C₃×D₃₅	C₃
cosocle	C₅×C₇×C₁₉⋊C₃	C₂×C₃
LCS	G ▷ C₅×C₇×C₁₉
UCS	C₁

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

209 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃₅×AGL(1,𝔽₁₉), (C₅⋊AGL(1,𝔽₁₉))⋊D₇, D₅×D₇×#4296, …
maximal normal subgroup of	D₃₅×AGL(1,𝔽₁₉), (C₅⋊AGL(1,𝔽₁₉))⋊D₇, D₅×D₇×#4296, …
maximal quotient of	Dic₃₅×#4296, C₂×D₃₅×#4296

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11970, 77);