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D₃×#443 #79887

order	384
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

Splittings

Fitting	C₃×#443 ⋊ C₂
Sylow	C₃ ⋊ C₂×#443

Subgroups

	subgroup	G/H
center	C₈	D₃×D₄
commutator	C₃×C₄	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₃
Fitting	C₃×#443	C₂
socle	C₂×C₃	C₂×C₄×D₄
prime radical	D₃×#135	C₂
cosocle	C₂×C₃×C₄	C₂⁴
hypercenter	#443	D₃
hypocenter	C₃	C₂×#443
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #443

472 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:

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

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#1335, #10704972, D₃×#1336, …
maximal normal subgroup of	D₃×#1335, #10704972, D₃×#1336, …
maximal quotient of	D₃×C₈×D₈, D₃×C₈×SD₁₆, D₃×C₈×Q₁₆, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 12463);