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D₃×#95 #4663

order	192
automorphism	Aut(G) order 18432
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂⁵

Aliases

Splittings

Fitting	C₃×#95 ⋊ C₂
Sylow	C₃ ⋊ C₂×#95

Subgroups

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₃
commutator	C₂×C₃	C₂×C₄²
Fitting	C₃×#95	C₂
socle, cosocle	C₂³×C₃	C₂³
prime radical	C₂³×D₃	C₂²
hypercenter	#95	D₃
hypocenter	C₃	C₂×#95
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ #95

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 3 generators on 15 points:

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

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#327, #68302, D₃×#328, …
maximal normal subgroup of	D₃×#327, #68302, D₃×#328, …
maximal quotient of	D₃×#336, #68660, #68661, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 222);