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C₂×D₃×#87831 #72231197

order	4800
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

C₂×D₃×#87831

Splittings

Hall	C₃×C₅² ⋊ C₂²×C₂²⋊C₄
Sylow	C₅² ⋊ C₂×D₃×C₂²⋊C₄
Sylow	C₃ ⋊ C₂²×#87831

Subgroups

	subgroup	G/H
center, hypercenter	C₂²	D₃×D₅⋊AGL(1,𝔽₅)
commutator	C₂×C₃×C₅²	C₂³×C₄
Frattini	C₂	C₂×D₃×D₅⋊AGL(1,𝔽₅)
Fitting, socle	C₂²×C₃×C₅²	C₂²×C₄
prime radical	C₂²×D₃×D₅²	C₂
cosocle	C₂×C₃×C₅⋊D₅	C₂⁴
hypocenter	C₃×C₅²	C₂²×C₂²⋊C₄
LCS	G ▷ C₂×C₃×C₅² ▷ C₃×C₅²
UCS	C₁ ◁ C₂²

3168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 120

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₃×#11717375, C₂×C₃⋊D₃×#87831
maximal normal subgroup of	C₂×D₃×#11717375
maximal quotient of	D₃×#13103931, C₂×C₃⋊D₃×#87831

GAP

Past the SmallGroups library coverage — no SmallGroups id.