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C₂×#204 #902

order	96
isoclinism	isoclinic class of #204
automorphism	Aut(G) = D₃×#3484 (order 768) · Inn(G) = D₁₂ · Out(G) = C₂²×D₄
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

Splittings

Fitting	C₂×C₃×C₈ ⋊ C₂
Sylow	C₃ ⋊ C₂×SD₁₆

Subgroups

	subgroup	G/H
center	C₂²	D₁₂
commutator, cosocle	C₃×C₄	C₂³
Frattini	C₄	C₂²×D₃
Fitting	C₂×C₃×C₈	C₂
socle	C₂²×C₃	D₄
prime radical	C₂×D₁₂	C₂
hypercenter	C₂×C₈	D₃
hypocenter	C₃	C₂×SD₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 13
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 3 generators on 13 points:

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

Conjugacy classes & character table

30 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₄×#204, #4693, #4696, …
maximal normal subgroup of	C₄×#204, #4693, #4696, …
maximal quotient of	#4680, #4681, C₄×#204, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(96, 109);