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D₃×#471 #80928

order	384
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

Splittings

Fitting	C₃×#471 ⋊ C₂
Sylow	C₃ ⋊ C₂×#471

Subgroups

	subgroup	G/H
center	C₂	D₃×#121
commutator, cosocle	C₂×C₃×C₄	C₂⁴
Frattini	C₂×C₄	C₂³×D₃
Fitting	C₃×#471	C₂
socle	C₂×C₃	C₂×#121
prime radical	D₃×AGL(1,ℤ/8)	C₂
hypercenter	#471	D₃
hypocenter	C₃	C₂×#471
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #471

468 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 4 generators on 19 points:

(1,3)(2,7)(4,10)(5,11)(6,13)(8,16)(9,12)(14,15)(17,18,19);(1,2,4,6,5,8,12,14)(3,7,10,13,11,16,9,15);(2,6)(3,9)(4,12)(8,14)(10,11)(13,15);(18,19)

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₃×#471, D₃×#3067, D₃×#3068, …
maximal normal subgroup of	C₂×D₃×#471, D₃×#3067, D₃×#3068, …
maximal quotient of	D₃×#1665, D₃×#1671, D₃×#1681, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 13504);