Finite Group Databasebeta

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C₂×C₃⋊D₃×#87830 #72231103

order	14400
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁵×C₃×C₄

Aliases

C₂×C₃⋊D₃×#87830

Splittings

derived, Hall	C₃²×C₅² ⋊ C₂²×C₄²
Sylow	C₅² ⋊ C₂×C₄²×C₃⋊D₃
Sylow	C₃² ⋊ C₂²×#87830

Subgroups

	subgroup	G/H
center, hypercenter	C₂²	C₃⋊D₃×D₅⋊AGL(1,𝔽₅)
commutator, hypocenter	C₃²×C₅²	C₂²×C₄²
Frattini	C₂	C₂×C₃⋊D₃×D₅⋊AGL(1,𝔽₅)
Fitting, socle	C₂²×C₃²×C₅²	C₂²×C₄
prime radical	C₂²×C₃⋊D₃×C₅⋊D₅	C₂²
cosocle	C₂×C₃²×C₅⋊D₅	C₂⁴
LCS	G ▷ C₃²×C₅²
UCS	C₁ ◁ C₂²

7392 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	#72231278, C₂×C₃⋊D₃×#11717375
maximal normal subgroup of	#72231278, C₂×C₃⋊D₃×#11717375

GAP

Past the SmallGroups library coverage — no SmallGroups id.