Finite Group Databasebeta

← Prev (#72220074) Next (#72220076) →

C₃×#11864777 #72220075

order	3456
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃ · Schur multiplier (H₂) = C₂⁶

Aliases

C₃×#11864777

Splittings

Fitting	C₃³×#127 ⋊ C₂²
Sylow	C₃³ ⋊ C₂×#453

Subgroups

	subgroup	G/H
center	C₂×C₃	#10595278
commutator, cosocle	C₂×C₃²×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂²×C₃×D₃²
Fitting	C₃³×#127	C₂²
socle	C₂×C₃³	C₂×#120
hypercenter	C₃×#127	D₃²
hypocenter	C₃²	C₂×C₃×#453
LCS	G ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#127

4318 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#72220090
maximal normal subgroup of	D₃×#11864777
maximal quotient of	#72220090

GAP

Past the SmallGroups library coverage — no SmallGroups id.