Dic₅₅₄₇ #36370787

order	22188
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₅₅₄₇
unambiguous semidirect product	C₃⋊Dic₁₈₄₉
unambiguous semidirect product	C₁₈₄₉⋊Dic₃

Splittings

derived, Hall	C₃×C₁₈₄₉ ⋊ C₄
Sylow	C₁₈₄₉ ⋊ Dic₃
Sylow	C₃ ⋊ Dic₁₈₄₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₅₅₄₇
commutator, hypocenter	C₃×C₁₈₄₉	C₄
Frattini	C₂×C₄₃	D₁₂₉
Fitting, cosocle	C₂×C₃×C₁₈₄₉	C₂
socle, prime radical	C₂×C₃×C₄₃	D₄₃
LCS	G ▷ C₃×C₁₈₄₉
UCS	C₁ ◁ C₂

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1856
transitive degree	μ_t(G) = 22188

A minimal faithful permutation representation — 2 generators on 1856 points:

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Polycyclic presentation:

2,3,43,2,43|a^2=d,c^43=e^42,b^a=b^2,c^a=c^42e,e^a=e^42

Conjugacy classes & character table

5550 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Dic₁₁₀₉₄
maximal normal subgroup of	Dic₁₁₀₉₄

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22188, 6);

Dic5547 #36370787