Dic₉₁₁₅ #49140683

order	36460
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₉₁₁₅
unambiguous semidirect product	C₁₈₂₃⋊Dic₅

Splittings

derived, Hall	C₅×C₁₈₂₃ ⋊ C₄
Sylow	C₁₈₂₃ ⋊ Dic₅
Sylow	C₅ ⋊ Dic₁₈₂₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₉₁₁₅
commutator, hypocenter	C₅×C₁₈₂₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₅×C₁₈₂₃	C₂
LCS	G ▷ C₅×C₁₈₂₃
UCS	C₁ ◁ C₂

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1832
transitive degree	μ_t(G) = 36460

A minimal faithful permutation representation — 2 generators on 1832 points:

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Polycyclic presentation:

2,5,1823,2|a^2=d,b^a=b^4,c^a=c^1822

Conjugacy classes & character table

9118 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36460, 4);

Dic9115 #49140683