Finite Group Databasebeta

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C₂×C₃⋊D₃×AGL(1,𝔽₁₇) #72276017

order	9792
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆ · Schur multiplier (H₂) = C₂³×C₃

Aliases

C₂×C₃⋊D₃×AGL(1,𝔽₁₇)

Splittings

Fitting, socle	C₂×C₃²×C₁₇ ⋊ C₂×C₁₆
derived, Hall	C₃²×C₁₇ ⋊ C₂²×C₁₆
Sylow	C₁₇ ⋊ C₂×C₁₆×C₃⋊D₃
Sylow	C₃² ⋊ C₂²×AGL(1,𝔽₁₇)

Subgroups

	subgroup	G/H
center, hypercenter	C₂	C₃⋊D₃×AGL(1,𝔽₁₇)
commutator, hypocenter	C₃²×C₁₇	C₂²×C₁₆
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₇	C₂×C₁₆
prime radical	C₂×C₃⋊D₃×D₁₇	C₈
cosocle	C₃²×#3633	C₂³
LCS	G ▷ C₃²×C₁₇
UCS	C₁ ◁ C₂

588 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 306

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.