Finite Group Databasebeta

← Prev (#72255381) Next (#72255383) →

C₂×D₃×#13658 #72255382

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

C₂×D₃×#13658

Splittings

Fitting	C₂×C₃×#13658 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#13658

Subgroups

	subgroup	G/H
center	C₂²	D₃×#2177
commutator	C₃×C₁₆	C₂⁴×C₄
Frattini	C₂×C₁₆	C₂⁴×D₃
Fitting	C₂×C₃×#13658	C₂
socle	C₂²×C₃	C₂×#2177
prime radical	C₂×D₃×#2263	C₂
cosocle	C₂×C₃×C₁₆	C₂⁵
hypercenter	C₂×#13658	D₃
hypocenter	C₃	C₂²×#13658
LCS	G ▷ C₃×C₁₆ ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#346 ◁ C₂×#13658

5434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 192

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₃×AGL(1,ℤ/32)
maximal normal subgroup of	C₂×D₃×AGL(1,ℤ/32)

GAP

Past the SmallGroups library coverage — no SmallGroups id.