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C₂×D₃×#1368 #72245707

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂×D₃×#1368

Splittings

Fitting	C₂×C₃×#1368 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#1368

Subgroups

	subgroup	G/H
center	C₂³	D₃×#106
commutator	C₃×C₈	C₂³×C₈
Frattini	C₄×C₈	C₂³×D₃
Fitting	C₂×C₃×#1368	C₂
socle	C₂³×C₃	C₂×#106
prime radical	C₂³×D₃	#106
cosocle	C₃×C₄×C₈	C₂⁴
hypercenter	C₂×#1368	D₃
hypocenter	C₃	C₂²×#1368
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#1368

1204 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 768

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₃×#12067, C₂×C₃⋊D₃×#1368, C₂×D₃×#7457, …
maximal normal subgroup of	C₂×D₃×#12067, C₂×D₃×#7457, C₂×D₃×#7389
maximal quotient of	C₂×C₃⋊D₃×#1368, C₂×D₃×#7457

GAP

Past the SmallGroups library coverage — no SmallGroups id.