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D₃×#65800 #14319817

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

Splittings

Fitting	C₂⁴×C₃×C₅ ⋊ C₂×C₄
Hall	C₃×C₅ ⋊ C₂×#379
Sylow	C₅ ⋊ D₃×#379
Sylow	C₃ ⋊ C₂×#65800

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃×AGL(1,𝔽₅)
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₂⁴×C₃×C₅	C₂×C₄
prime radical	C₂⁴×D₃×D₅	C₂
cosocle	C₂²×C₃×D₅	C₂⁴
hypercenter	C₂⁴	D₃×AGL(1,𝔽₅)
hypocenter	C₃×C₅	C₂×#379
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂⁴

6928 conjugacy classes of subgroups; only the 434 normal subgroups are shown.

normal subgroups only

This group has 6928 conjugacy classes of subgroups — too many to draw. Only its 434 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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	D₃×AGL(1,𝔽₅)×#120, D₃×#10604461, D₃×#11757174, …
maximal normal subgroup of	D₃×AGL(1,𝔽₅)×#120, D₃×#10604461
maximal quotient of	D₃×#10605017, D₃×#10605015, C₃⋊D₃×#65800

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45515);