Finite Group Databasebeta

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C₂×D₃×#7310 #72270524

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

C₂×D₃×#7310

Splittings

Fitting	C₂×C₃×#7310 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#7310

Subgroups

	subgroup	G/H
center	C₂²	D₃×#1304
commutator	C₂⁴×C₃	C₂²×C₄²
Frattini	C₂³×D₄	C₂³×D₃
Fitting	C₂×C₃×#7310	C₂
socle	C₂²×C₃	C₂×#1304
prime radical	C₂⁴×D₃×D₄	C₂²
cosocle	C₂³×C₃×D₄	C₂⁴
hypercenter	C₂×#7310	D₃
hypocenter	C₃	C₂²×#7310
LCS	G ▷ C₂⁴×C₃ ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂⁴×D₄ ◁ C₂×#7310

37306 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#72219160, D₃×#72218521, D₃×#72219158
maximal normal subgroup of	D₃×#72219160, D₃×#72218521, D₃×#72219158

GAP

Past the SmallGroups library coverage — no SmallGroups id.