D₉₄₄₅ #34038530

order	18890
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₉₄₄₅
unambiguous semidirect product	C₅⋊D₁₈₈₉
unambiguous semidirect product	C₁₈₈₉⋊D₅

Splittings

Fitting, socle, derived, Hall	C₅×C₁₈₈₉ ⋊ C₂
Sylow	C₁₈₈₉ ⋊ D₅
Sylow	C₅ ⋊ D₁₈₈₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₈₈₉	C₂
LCS	G ▷ C₅×C₁₈₈₉
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1894
transitive degree	μ_t(G) = 9445

A minimal faithful permutation representation — 2 generators on 1894 points:

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Polycyclic presentation:

2,5,1889|b^a=b^4,c^a=c^1888

Conjugacy classes & character table

4724 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	#49180164, #49180165, D₅×D₁₈₈₉, …
maximal normal subgroup of	#49180164, #49180165, D₅×D₁₈₈₉, …
maximal quotient of	Dic₉₄₄₅, C₂×D₉₄₄₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18890, 3);

D9445 #34038530