D₈₉₄₅ #31821981

order	17890
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₈₉₄₅
unambiguous semidirect product	C₅⋊D₁₇₈₉
unambiguous semidirect product	C₁₇₈₉⋊D₅

Splittings

Fitting, socle, derived, Hall	C₅×C₁₇₈₉ ⋊ C₂
Sylow	C₁₇₈₉ ⋊ D₅
Sylow	C₅ ⋊ D₁₇₈₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₇₈₉	C₂
LCS	G ▷ C₅×C₁₇₈₉
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1794
transitive degree	μ_t(G) = 8945

A minimal faithful permutation representation — 2 generators on 1794 points:

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Polycyclic presentation:

2,5,1789|b^a=b^4,c^a=c^1788

Conjugacy classes & character table

4474 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	#49088777, #49088778, D₅×D₁₇₈₉, …
maximal normal subgroup of	#49088777, #49088778, D₅×D₁₇₈₉, …
maximal quotient of	Dic₈₉₄₅, C₂×D₈₉₄₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17890, 3);

D8945 #31821981