Dic₅₇₂₁ #37504289

order	22884
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₅₇₂₁
unambiguous semidirect product	C₃⋊Dic₁₉₀₇
unambiguous semidirect product	C₁₉₀₇⋊Dic₃

Splittings

derived, Hall	C₃×C₁₉₀₇ ⋊ C₄
Sylow	C₁₉₀₇ ⋊ Dic₃
Sylow	C₃ ⋊ Dic₁₉₀₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅₇₂₁
commutator, hypocenter	C₃×C₁₉₀₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₁₉₀₇	C₂
LCS	G ▷ C₃×C₁₉₀₇
UCS	C₁ ◁ C₂

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1914
transitive degree	μ_t(G) = 22884

A minimal faithful permutation representation — 2 generators on 1914 points:

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Polycyclic presentation:

2,3,1907,2|a^2=d,b^a=b^2,c^a=c^1906

Conjugacy classes & character table

5724 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Dic₁₁₄₄₂
maximal normal subgroup of	Dic₁₁₄₄₂

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22884, 4);

Dic5721 #37504289