D₈₃₁₅ #30659052

order	16630
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₈₃₁₅
unambiguous semidirect product	C₅⋊D₁₆₆₃
unambiguous semidirect product	C₁₆₆₃⋊D₅

Splittings

Fitting, socle, derived, Hall	C₅×C₁₆₆₃ ⋊ C₂
Sylow	C₁₆₆₃ ⋊ D₅
Sylow	C₅ ⋊ D₁₆₆₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₆₆₃	C₂
LCS	G ▷ C₅×C₁₆₆₃
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1668
transitive degree	μ_t(G) = 8315

A minimal faithful permutation representation — 2 generators on 1668 points:

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Polycyclic presentation:

2,5,1663|b^a=b^4,c^a=c^1662

Conjugacy classes & character table

4159 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₅×D₁₆₆₃, C₂×D₈₃₁₅
maximal normal subgroup of	D₅×D₁₆₆₃, C₂×D₈₃₁₅
maximal quotient of	Dic₈₃₁₅, C₂×D₈₃₁₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16630, 3);

D8315 #30659052