Finite Group Databasebeta

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C₂×D₃×#1304 #72270033

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁹

Aliases

C₂×D₃×#1304

Splittings

Fitting	C₂×C₃×#1304 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#1304

Subgroups

	subgroup	G/H
center	C₂³	D₃×#95
commutator	C₂³×C₃	C₂²×C₄²
Frattini	C₂⁵	C₂³×D₃
Fitting	C₂×C₃×#1304	C₂
socle	C₂³×C₃	C₂×#95
prime radical	C₂⁶×D₃	C₂²
cosocle	C₂⁵×C₃	C₂⁴
hypercenter	C₂×#1304	D₃
hypocenter	C₃	C₂²×#1304
LCS	G ▷ C₂³×C₃ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂⁶ ◁ C₂×#1304

20820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#111458, D₃×#115133, C₂×D₃×#10336, …
maximal normal subgroup of	D₃×#111458, D₃×#115133, C₂×D₃×#10336, …
maximal quotient of	C₂×D₃×#7310, C₂×D₃×#7307, D₃×C₂²⋊#1304, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.