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C₂×#3787 #64281

order	288
isoclinism	isoclinic class of #157
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³×C₃

Aliases

Splittings

C₃² ⋊ C₂²×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄	#157
commutator, hypocenter	C₃²	C₂²×C₈
Frattini	C₂	C₂²×#157
Fitting	C₂×C₃²×C₄	C₄
socle	C₂²×C₃²	C₂×C₄
prime radical	C₂²×C₃⋊D₃	C₄
cosocle	C₃⋊Dic₃	C₂³
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₄

130 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:

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

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10590043, #10590051, #10590090, …
maximal normal subgroup of	#10590043, #10590051, #10590090, …
maximal quotient of	C₄×#3787, #10593725, #10593726, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 929);