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D₃×#1312 #10704172

order	768
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₆ · Schur multiplier (H₂) = C₂²×C₄

Aliases

Splittings

Fitting	C₃×#1312 ⋊ C₂
Sylow	C₃ ⋊ C₂×#1312

Subgroups

	subgroup	G/H
center, Frattini	C₄×C₈	C₂²×D₃
commutator	C₂×C₃	C₂×C₄×C₁₆
Fitting	C₃×#1312	C₂
socle	C₂²×C₃	C₂×C₄×C₈
prime radical	C₂²×D₃	C₄×C₈
cosocle	C₃×C₄×C₈	C₂³
hypercenter	#1312	D₃
hypocenter	C₃	C₂×#1312
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₈ ◁ #1312

350 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 384

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#11402, D₃×#7053, D₃×#12062, …
maximal normal subgroup of	D₃×#11402, D₃×#7053, D₃×#12062, …
maximal quotient of	D₃×#7053, D₃×#7332, C₃⋊D₃×#1312

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 78553);