D₅₆₀₁ #26014205

order	11202
automorphism	Aut(G) order 20902932
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₅₆₀₁
unambiguous semidirect product	C₃⋊D₁₈₆₇
unambiguous semidirect product	C₁₈₆₇⋊D₃

Splittings

Fitting, socle, derived, Hall	C₃×C₁₈₆₇ ⋊ C₂
Sylow	C₁₈₆₇ ⋊ D₃
Sylow	C₃ ⋊ D₁₈₆₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₈₆₇	C₂
LCS	G ▷ C₃×C₁₈₆₇
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1870
transitive degree	μ_t(G) = 5601

A minimal faithful permutation representation — 2 generators on 1870 points:

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Polycyclic presentation:

2,3,1867|b^a=b^2,c^a=c^1866

Conjugacy classes & character table

2802 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×D₁₈₆₇, C₂×D₅₆₀₁, D₁₆₈₀₃, …
maximal normal subgroup of	D₃×D₁₈₆₇, C₂×D₅₆₀₁, C₃⋊(D₁₈₆₇⋊C₃), …
maximal quotient of	Dic₅₆₀₁, C₂×D₅₆₀₁, D₁₆₈₀₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11202, 5);

D5601 #26014205