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D₃×#446 #79957

order	384
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁴

Aliases

Splittings

Fitting	C₃×#446 ⋊ C₂
Sylow	C₃ ⋊ C₂×#446

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₃
commutator, socle	C₂²×C₃	C₂³×C₄
Fitting	C₃×#446	C₂
prime radical	C₂²×D₃	C₂²×C₄
cosocle	C₂×C₃×C₄	C₂⁴
hypercenter	#446	D₃
hypocenter	C₃	C₂×#446
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ #446

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 192

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

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

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#1338, #10705008, #10705148, …
maximal normal subgroup of	D₃×#1338, #10705008, #10705148, …
maximal quotient of	D₃×#1771, D₃×#1770, #10793808, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 12533);