Dic₆₂₄₃ #38735846

order	24972
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₆₂₄₃
unambiguous semidirect product	C₃⋊Dic₂₀₈₁

Splittings

derived, Hall	C₃×C₂₀₈₁ ⋊ C₄
Sylow	C₂₀₈₁ ⋊ Dic₃
Sylow	C₃ ⋊ Dic₂₀₈₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₆₂₄₃
commutator, hypocenter	C₃×C₂₀₈₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₂₀₈₁	C₂
LCS	G ▷ C₃×C₂₀₈₁
UCS	C₁ ◁ C₂

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 2088
transitive degree	μ_t(G) = 24972

A minimal faithful permutation representation — 2 generators on 2088 points:

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Polycyclic presentation:

2,3,2081,2|a^2=d,b^a=b^2,c^a=c^2080

Conjugacy classes & character table

6246 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Dic₁₂₄₈₆
maximal normal subgroup of	Dic₁₂₄₈₆

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24972, 4);

Dic6243 #38735846