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C₂×D₇×C₁₁²⋊C₃ #23779043

order	10164
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂×C₁₁

Aliases

C₂×D₇×C₁₁²⋊C₃

Splittings

Fitting, socle	C₂×C₇×C₁₁² ⋊ C₂×C₃
derived, Hall	C₇×C₁₁² ⋊ C₂²×C₃
Hall	C₂×C₁₁²×D₇ ⋊ C₃
Hall	C₇×C₁₁²⋊C₃ ⋊ C₂²
Sylow	C₁₁² ⋊ C₂×C₃×D₇
Sylow	C₇ ⋊ C₂²×C₁₁²⋊C₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₇×C₁₁²⋊C₃
commutator, cosocle, hypocenter	C₇×C₁₁²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₁²	C₂×C₃
LCS	G ▷ C₇×C₁₁²
UCS	C₁ ◁ C₂

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

430 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×AGL(1,𝔽₇)×C₁₁²⋊C₃, D₃×D₇×C₁₁²⋊C₃, C₂×C₃×D₇×C₁₁²⋊C₃, …
maximal normal subgroup of	C₂×AGL(1,𝔽₇)×C₁₁²⋊C₃, C₂×C₃×D₇×C₁₁²⋊C₃
maximal quotient of	C₂×D₇×C₁₁²⋊C₉, D₃×D₇×C₁₁²⋊C₃, C₂×C₃×D₇×C₁₁²⋊C₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10164, 95);