Dic₆₄₈₃ #39906255

order	25932
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₆₄₈₃
unambiguous semidirect product	C₃⋊Dic₂₁₆₁

Splittings

derived, Hall	C₃×C₂₁₆₁ ⋊ C₄
Sylow	C₂₁₆₁ ⋊ Dic₃
Sylow	C₃ ⋊ Dic₂₁₆₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₆₄₈₃
commutator, hypocenter	C₃×C₂₁₆₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₂₁₆₁	C₂
LCS	G ▷ C₃×C₂₁₆₁
UCS	C₁ ◁ C₂

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 2168
transitive degree	μ_t(G) = 25932

A minimal faithful permutation representation — 2 generators on 2168 points:

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Polycyclic presentation:

2,3,2161,2|a^2=d,b^a=b^2,c^a=c^2160

Conjugacy classes & character table

6486 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Dic₁₂₉₆₆
maximal normal subgroup of	Dic₁₂₉₆₆

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25932, 6);

Dic6483 #39906255