Dic₈₇₉₅ #47976027

order	35180
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₈₇₉₅
unambiguous semidirect product	C₁₇₅₉⋊Dic₅

Splittings

derived, Hall	C₅×C₁₇₅₉ ⋊ C₄
Sylow	C₁₇₅₉ ⋊ Dic₅
Sylow	C₅ ⋊ Dic₁₇₅₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₈₇₉₅
commutator, hypocenter	C₅×C₁₇₅₉	C₄
Fitting, socle, prime radical, cosocle	C₂×C₅×C₁₇₅₉	C₂
LCS	G ▷ C₅×C₁₇₅₉
UCS	C₁ ◁ C₂

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1768
transitive degree	μ_t(G) = 35180

A minimal faithful permutation representation — 2 generators on 1768 points:

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Polycyclic presentation:

2,5,1759,2|a^2=d,b^a=b^4,c^a=c^1758

Conjugacy classes & character table

8798 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35180, 4);

Dic8795 #47976027