Dic₅₈₄₇ #37552669

order	23388
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₅₈₄₇
unambiguous semidirect product	C₃⋊Dic₁₉₄₉

Splittings

derived, Hall	C₃×C₁₉₄₉ ⋊ C₄
Sylow	C₁₉₄₉ ⋊ Dic₃
Sylow	C₃ ⋊ Dic₁₉₄₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₅₈₄₇
commutator, hypocenter	C₃×C₁₉₄₉	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₁₉₄₉	C₂
LCS	G ▷ C₃×C₁₉₄₉
UCS	C₁ ◁ C₂

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1956
transitive degree	μ_t(G) = 23388

A minimal faithful permutation representation — 2 generators on 1956 points:

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Polycyclic presentation:

2,3,1949,2|a^2=d,b^a=b^2,c^a=c^1948

Conjugacy classes & character table

5850 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Dic₁₁₆₉₄
maximal normal subgroup of	Dic₁₁₆₉₄

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23388, 4);

Dic5847 #37552669