D₅₇₃₉ #26039764

order	11478
automorphism	Aut(G) order 21945936
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₅₇₃₉
unambiguous semidirect product	C₃⋊D₁₉₁₃
unambiguous semidirect product	C₁₉₁₃⋊D₃

Splittings

Fitting, socle, derived, Hall	C₃×C₁₉₁₃ ⋊ C₂
Sylow	C₁₉₁₃ ⋊ D₃
Sylow	C₃ ⋊ D₁₉₁₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₉₁₃	C₂
LCS	G ▷ C₃×C₁₉₁₃
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1916
transitive degree	μ_t(G) = 5739

A minimal faithful permutation representation — 2 generators on 1916 points:

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Polycyclic presentation:

2,3,1913|b^a=b^2,c^a=c^1912

Conjugacy classes & character table

2871 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×D₁₉₁₃, C₂×D₅₇₃₉, D₁₇₂₁₇, …
maximal normal subgroup of	D₃×D₁₉₁₃, C₂×D₅₇₃₉, C₃×D₅₇₃₉
maximal quotient of	Dic₅₇₃₉, C₂×D₅₇₃₉, D₁₇₂₁₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11478, 3);

D5739 #26039764