D₅₉₃₇ #26045167

order	11874
automorphism	Aut(G) order 23486772
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₅₉₃₇
unambiguous semidirect product	C₃⋊D₁₉₇₉
unambiguous semidirect product	C₁₉₇₉⋊D₃

Splittings

Fitting, socle, derived, Hall	C₃×C₁₉₇₉ ⋊ C₂
Sylow	C₁₉₇₉ ⋊ D₃
Sylow	C₃ ⋊ D₁₉₇₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₉₇₉	C₂
LCS	G ▷ C₃×C₁₉₇₉
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1982
transitive degree	μ_t(G) = 5937

A minimal faithful permutation representation — 2 generators on 1982 points:

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Polycyclic presentation:

2,3,1979|b^a=b^2,c^a=c^1978

Conjugacy classes & character table

2970 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×D₁₉₇₉, C₂×D₅₉₃₇, D₁₇₈₁₁, …
maximal normal subgroup of	D₃×D₁₉₇₉, C₂×D₅₉₃₇, C₃×D₅₉₃₇
maximal quotient of	Dic₅₉₃₇, C₂×D₅₉₃₇, D₁₇₈₁₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11874, 3);

D5937 #26045167