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C₃×D₇×C₁₇×ΓL(1,𝔽₈) #28418399

order	14994
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₁₇ · Schur multiplier (H₂) = C₃

Aliases

C₃×D₇×C₁₇×ΓL(1,𝔽₈)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₇	D₇×ΓL(1,𝔽₈)
commutator, cosocle, hypocenter	C₇²	C₂×C₃²×C₁₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₇	C₂×C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃×C₁₇

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2142

Conjugacy classes & character table

1275 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×D₇×C₁₇×AGL(1,𝔽₇), C₃×D₇×C₁₇⋊AGL(1,𝔽₇), C₃×D₇×ΓL(1,𝔽₈)×D₁₇, …
maximal normal subgroup of	C₃×D₇×C₁₇×AGL(1,𝔽₇), C₃×D₇×C₁₇⋊AGL(1,𝔽₇), C₃×D₇×ΓL(1,𝔽₈)×D₁₇, …
maximal quotient of	C₃×C₁₇×ΓL(1,𝔽₈)×Dic₇, C₂×C₃×D₇×C₁₇×ΓL(1,𝔽₈)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14994, 91);