Finite Group Databasebeta

← Prev (#72270978) Next (#72270980) →

D₃×#72214565 #72270979

order	6144
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹³

Aliases

D₃×#72214565

Splittings

Fitting	C₃×#72214565 ⋊ C₂
Sylow	C₃ ⋊ C₂×#72214565

Subgroups

	subgroup	G/H
center	C₂²	D₃×#32898
commutator, cosocle	C₂²×C₃×#41	C₂⁵
Frattini	C₂²×#41	C₂⁴×D₃
Fitting	C₃×#72214565	C₂
socle	C₂²×C₃	C₂×#32898
hypercenter	#72214565	D₃
hypocenter	C₃	C₂×#72214565
LCS	G ▷ C₂²×C₃×#41 ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×H(5,𝔽₂) ◁ #72214565

Only the 2045 normal subgroups are shown; non-normal subgroups are omitted.

Full subgroup data →

Conjugacy classes & character table

237 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.