Finite Group Databasebeta

← Prev (#72259493) Next (#72259495) →

C₃⋊D₃×#11717375 #72259494

order	14400
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶×C₃

Aliases

C₃⋊D₃×#11717375

Splittings

Fitting	C₂²×C₃²×C₅² ⋊ C₂²×C₄
Hall	C₃²×C₅² ⋊ C₂×C₄×D₄
Sylow	C₅² ⋊ C₄×D₄×C₃⋊D₃
Sylow	C₃² ⋊ C₂×#11717375

Subgroups

	subgroup	G/H
center, Frattini	C₂	C₂×C₃⋊D₃×D₅⋊AGL(1,𝔽₅)
commutator, socle	C₂×C₃²×C₅²	C₂³×C₄
Fitting	C₂²×C₃²×C₅²	C₂²×C₄
prime radical	C₃⋊D₃×#87886	C₂
cosocle	C₂×C₃²×C₅⋊D₅	C₂⁴
hypercenter	C₂²	C₃⋊D₃×D₅⋊AGL(1,𝔽₅)
hypocenter	C₃²×C₅²	C₂×C₄×D₄
LCS	G ▷ C₂×C₃²×C₅² ▷ C₃²×C₅²
UCS	C₁ ◁ C₂ ◁ C₂²

6528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 180

Conjugacy classes & character table

228 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₃⋊D₃×#11717375
maximal normal subgroup of	C₂×C₃⋊D₃×#11717375
maximal quotient of	C₂×C₃⋊D₃×#11717375

GAP

Past the SmallGroups library coverage — no SmallGroups id.