D₅₉₁₉ #26044844

order	11838
automorphism	Aut(G) order 23344536
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₅₉₁₉
unambiguous semidirect product	C₃⋊D₁₉₇₃
unambiguous semidirect product	C₁₉₇₃⋊D₃

Splittings

Fitting, socle, derived, Hall	C₃×C₁₉₇₃ ⋊ C₂
Sylow	C₁₉₇₃ ⋊ D₃
Sylow	C₃ ⋊ D₁₉₇₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₉₇₃	C₂
LCS	G ▷ C₃×C₁₉₇₃
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1976
transitive degree	μ_t(G) = 5919

A minimal faithful permutation representation — 2 generators on 1976 points:

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Polycyclic presentation:

2,3,1973|b^a=b^2,c^a=c^1972

Conjugacy classes & character table

2961 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×D₁₉₇₃, C₂×D₅₉₁₉, D₁₇₇₅₇, …
maximal normal subgroup of	D₃×D₁₉₇₃, C₂×D₅₉₁₉, C₃×D₅₉₁₉
maximal quotient of	Dic₅₉₁₉, C₂×D₅₉₁₉, D₁₇₇₅₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11838, 3);

D5919 #26044844