Finite Group Databasebeta

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C₃×#10948634 #72222758

order	2304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

C₃×#10948634

Splittings

Fitting	C₃²×AGL(1,ℤ/16) ⋊ C₂
Sylow	C₃² ⋊ #33468

Subgroups

	subgroup	G/H
center	C₂×C₃	D₃×#442
commutator	C₃×C₈	C₂³×C₃×C₄
Frattini	C₂×C₈	C₂³×C₃×D₃
Fitting	C₃²×AGL(1,ℤ/16)	C₂
socle	C₂×C₃²	C₂×#442
prime radical	C₃×#82035	C₂
cosocle	C₂×C₃×C₈	C₂⁴×C₃
hypercenter	C₃×AGL(1,ℤ/16)	D₃
hypocenter	C₃	C₃×#33468
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#97 ◁ C₃×AGL(1,ℤ/16)

1381 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

207 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×#72228227
maximal normal subgroup of	C₃×#72228227

GAP

Past the SmallGroups library coverage — no SmallGroups id.