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C₃×PSU(3,𝔽₂)⋊C₁₆ #72218964

order	3456
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

C₃×PSU(3,𝔽₂)⋊C₁₆

Splittings

C₃³ ⋊ Q₈⋊C₁₆

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₈	AΓL(1,𝔽₉)
commutator	#157	C₂×C₃×C₁₆
Frattini	C₈	C₃×AΓL(1,𝔽₉)
Fitting	C₃³×C₈	SD₁₆
socle	C₂×C₃³	Q₈⋊C₈
prime radical	C₂×C₃×C₃⋊D₃	C₂²⋊C₈
cosocle	C₈×#157	C₂²×C₃
hypocenter	C₃²	C₃×Q₈⋊C₁₆
LCS	G ▷ #157 ▷ C₃⋊D₃ ▷ C₃²
UCS	C₁ ◁ C₃×C₈

226 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 64 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

216 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×#72218959, C₃×C₁₆×AΓL(1,𝔽₉)
maximal normal subgroup of	C₃×C₁₆×AΓL(1,𝔽₉)
maximal quotient of	C₃×#72219099

GAP

Past the SmallGroups library coverage — no SmallGroups id.