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C₂×#3775 #64238

order	288
isoclinism	isoclinic class of #3774
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

Splittings

C₃² ⋊ C₂×SD₁₆

Subgroups

	subgroup	G/H
center, hypercenter	C₂²	GO⁺(4,𝔽₂)
commutator, cosocle	C₃⋊Dic₃	C₂³
Frattini	C₂	C₂×GO⁺(4,𝔽₂)
Fitting, socle	C₂²×C₃²	D₄
prime radical	C₂×#625	C₂
hypocenter	C₃²	C₂×SD₁₆
LCS	G ▷ C₃⋊Dic₃ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²

114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 3 generators on 16 points:

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

Conjugacy classes & character table

30 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10593352, #10593354, #10593355, …
maximal normal subgroup of	#10593352, #10593354, #10593355, …
maximal quotient of	#10593359, #10593366, #10593376, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 886);