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D₃×#430 #79259

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

Aliases

Splittings

Fitting	C₃×#430 ⋊ C₂
Sylow	C₃ ⋊ C₂×#430

Subgroups

	subgroup	G/H
center	C₄	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₃
Fitting	C₃×#430	C₂
socle	C₂×C₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₃	Q₈
cosocle	C₂×C₃×C₄	C₂⁴
hypercenter	#430	D₃
hypocenter	C₃	C₂×#430
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #430

460 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:

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

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#1858, #10796031, D₃×#1861, …
maximal normal subgroup of	D₃×#1858, #10796031, D₃×#1861, …
maximal quotient of	D₃×#1565, #10764168, D₃×#1569, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 11835);