D₉₅₀₅ #34039622

order	19010
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₉₅₀₅
unambiguous semidirect product	C₅⋊D₁₉₀₁
unambiguous semidirect product	C₁₉₀₁⋊D₅

Splittings

Fitting, socle, derived, Hall	C₅×C₁₉₀₁ ⋊ C₂
Sylow	C₁₉₀₁ ⋊ D₅
Sylow	C₅ ⋊ D₁₉₀₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₉₀₁	C₂
LCS	G ▷ C₅×C₁₉₀₁
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1906
transitive degree	μ_t(G) = 9505

A minimal faithful permutation representation — 2 generators on 1906 points:

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Polycyclic presentation:

2,5,1901|b^a=b^4,c^a=c^1900

Conjugacy classes & character table

4754 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	#49184570, #49184571, D₅×D₁₉₀₁, …
maximal normal subgroup of	#49184570, #49184571, D₅×D₁₉₀₁, …
maximal quotient of	Dic₉₅₀₅, C₂×D₉₅₀₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19010, 5);

D9505 #34039622