Finite Group Databasebeta

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C₂×D₃×#12711 #72248104

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹²

Aliases

C₂×D₃×#12711

Splittings

Fitting	C₂×C₃×#12711 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#12711

Subgroups

	subgroup	G/H
center	C₂²	D₃×#1781
commutator	C₂²×C₃×C₄	C₂⁴×C₄
Frattini	C₂×#41	C₂⁴×D₃
Fitting	C₂×C₃×#12711	C₂
socle	C₂²×C₃	C₂×#1781
prime radical	C₂×D₃×#3484	C₂
cosocle	C₂×C₃×#41	C₂⁵
hypercenter	C₂×#12711	D₃
hypocenter	C₃	C₂²×#12711
LCS	G ▷ C₂²×C₃×C₄ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×H(5,𝔽₂) ◁ C₂×#12711

At least 9332 conjugacy classes of subgroups; only the 2279 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#72215601, D₃×#72214565
maximal normal subgroup of	D₃×#72215601, D₃×#72214565

GAP

Past the SmallGroups library coverage — no SmallGroups id.