Finite Group Databasebeta

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C₃×((C₃⋊D₃)⋊C₃)⋊C₁₆ #72218965

order	2592
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

C₃×((C₃⋊D₃)⋊C₃)⋊C₁₆

Splittings

derived	H(3,𝔽₃) ⋊ C₂×C₃×C₁₆
Sylow	C₃×H(3,𝔽₃) ⋊ C₂×C₁₆

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₈	((C₃⋊D₃)⋊C₃)⋊C₂
commutator, hypocenter	H(3,𝔽₃)	C₂×C₃×C₁₆
Frattini	C₃×C₈	C₃×D₃²
Fitting	C₃×C₈×H(3,𝔽₃)	C₂²
socle	C₂×C₃²	D₃×C₃⋊C₈
prime radical	C₂×C₃×(C₃⋊D₃)⋊C₃	C₈
cosocle	C₈×H(3,𝔽₃)	C₂²×C₃
LCS	G ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₃×C₈

301 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 301 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×#72218959, C₃×C₁₆×((C₃⋊D₃)⋊C₃)⋊C₂
maximal normal subgroup of	C₃×C₁₆×((C₃⋊D₃)⋊C₃)⋊C₂
maximal quotient of	C₃×((C₃⋊D₃)⋊C₃)⋊C₃₂

GAP

Past the SmallGroups library coverage — no SmallGroups id.