Finite Group Databasebeta

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C₂²×C₃⋊D₃×D₅⋊AGL(1,𝔽₅) #72230648

order	14400
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁰×C₃

Aliases

C₂²×C₃⋊D₃×D₅⋊AGL(1,𝔽₅)

Splittings

Fitting, socle	C₂²×C₃²×C₅² ⋊ C₂²×C₄
derived, Hall	C₃²×C₅² ⋊ C₂⁴×C₄
Sylow	C₅² ⋊ C₂³×C₄×C₃⋊D₃
Sylow	C₃² ⋊ C₂³×D₅⋊AGL(1,𝔽₅)

Subgroups

	subgroup	G/H
center, hypercenter	C₂²	C₃⋊D₃×D₅⋊AGL(1,𝔽₅)
commutator, hypocenter	C₃²×C₅²	C₂⁴×C₄
Frattini	C₁	G
Fitting, socle	C₂²×C₃²×C₅²	C₂²×C₄
prime radical	C₂²×D₅²×C₃⋊D₃	C₂
cosocle	C₃²×C₅⋊D₅	C₂⁵
LCS	G ▷ C₃²×C₅²
UCS	C₁ ◁ C₂²

17760 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 360

Conjugacy classes & character table

336 conjugacy classes. The character table is too large to display.

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.