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D₃×#432 #79330

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

Aliases

Splittings

Fitting	C₃×#432 ⋊ C₂
Sylow	C₃ ⋊ C₂×#432

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₃
commutator, socle	C₂²×C₃	C₂³×C₄
Fitting	C₃×#432	C₂
prime radical	C₂³×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴
hypercenter	#432	D₃
hypocenter	C₃	C₂×#432
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ #432

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 96

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

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

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#1285, #10684933, #10684937, …
maximal normal subgroup of	D₃×#1285, #10684933, #10684937, …
maximal quotient of	D₃×#1745, D₃×#1749, D₃×#1767, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 11906);